MCQExams
0:0:1
CBSE
JEE
NTSE
NEET
Practice
Homework
×
CBSE Questions for Class 8 Maths Squares And Square Roots Quiz 7 - MCQExams.com
CBSE
Class 8 Maths
Squares And Square Roots
Quiz 7
Find the value of $$\sqrt {25}$$.
Report Question
0%
$$5$$
0%
$$-\sqrt {5}$$
0%
$$\sqrt {3}$$
0%
None of these
Explanation
$$\sqrt {25} = \sqrt {5\times 5} = 5$$
State whether the statements are true (T) or false (F).
If $$a^2$$ ends in 9, then $$a^3$$ ends in 7.
Report Question
0%
True
0%
False
Explanation
$$\because (7)^2 = 49$$ ends in 9 and
$$(7)^3 = 343 $$ does not ends in 7.
Estimate: $$\sqrt { 60 } $$
Report Question
0%
$$7.7$$
0%
$$7$$
0%
$$7.2$$
0%
$$7.5$$
Explanation
$$60$$ is in between two perfect squares: $$49$$, which is $${7}^{2}$$ and $$64$$ which is $${8}^{2}$$. The difference between $$64$$ and $$49$$ is $$15$$ so $$60$$ is little more than $$\cfrac{2}{3}$$ of the way toward $$64$$ from $$49$$. A reasonable estimate for $$\sqrt {60}$$, then would be about $$7.7$$ which is a little more than $$\cfrac{2}{3}$$ toward $$8$$ from $$7$$.
$$127$$ is a
Report Question
0%
irrational number
0%
perfect square
number
0%
non-perfect square
number
0%
real number
Explanation
We know that the number ends with $$00, 1, 4, 5, 6$$ or $$9$$ are perfect square and natural number is also a real number.
So, 127 is a non-perfect square and a real number.
Identify which one of the following numbers are Pythagorean triplets?
Report Question
0%
$$12, 35, 37$$
0%
$$15, 102, 106$$
0%
$$10, 23, 26$$
0%
$$14, 28, 50$$
Explanation
Taking the case of $$12, 35, 37$$
On squaring each number, we get
$$12^2=144$$
$$35^2 = 1225$$
$$37^2=1369$$
Now, $$12^2+35^2 = 144 + 1225 = 1369$$
$$=37^2$$
$$\therefore 12^2+35^2=37^2$$
Hence, $$12, 35, 37$$ are Pythagorean triplets.
$$10,24$$ and __ will form a Pythagorean triplets.
Report Question
0%
$$25$$
0%
$$26$$
0%
$$27$$
0%
$$28$$
Explanation
We know that Pythagorean triplets will satisfy the condition, $$a^2+b^2=c^2$$
$$c^2=10^2+24^2\\=100+576\\=676$$
$$\Rightarrow c=26$$
Thus $$10, 24$$ and $$26$$ form a Pythagorean triplet
What is the Pythagorean triplets whose one member is $$20$$?
Report Question
0%
$$20, 97, 99$$
0%
$$20, 99, 101$$
0%
$$20, 197, 199$$
0%
$$20, 199, 201$$
Explanation
For any natural numbers $$m > 1, 2m$$, $$m^{2} - 1$$, $$m^{2} + 1$$ forms a Pythagorean triplet.
If we take $$m^2 + 1 = 20$$, then $$m^2 = 19$$
The value of m will not be an integer.
If we take $$m^2 - 1 = 20$$, then $$m^2 = 21$$
Again the value of m will not be an integer.
Let $$2m = 20$$
$$=> m = 10$$
$$\therefore 2m = 2 \cdot 10 = 20$$
$$m^{2} - 1$$ = $$10^{2} - 1=99$$
and
$$m^{2} + 1$$ = $$10^{2} + 1=101$$
Therefore, the Pythagorean triplets are $$20, 99, 101.$$
What least number must be added to $$4812$$ to make the sum a perfect square? (Use Long division method).
Report Question
0%
$$86$$
0%
$$88$$
0%
$$89$$
0%
$$85$$
Explanation
The following steps are used to find the square root by long division method:
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Repeat the process till the remainder becomes zero
Divisor
$$\downarrow$$
Quotient
$$\downarrow$$
$$69$$
$$6$$
$$\overline{48}$$ $$\overline{12}$$
$$\underline{36} \underline{\ }$$
$$129$$
$$1212$$
$$\underline{1161}$$
$$51$$
Here, the remainder $$=51$$
We observe here $$69^2 < 4812 < 70^2$$
The required number to be added $$=70^2 - 4812$$
$$= 4900 - 4812$$
$$= 88$$
Therefore, $$88$$ must be added to $$4812$$ to make it a perfect square.
Find the square root of $$12.25$$ using long division method.
Report Question
0%
$$3.2$$
0%
$$3.4$$
0%
$$3.5$$
0%
$$3.1$$
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Divisor
$$\downarrow$$
Quotient
$$\downarrow$$
3.5
3
$$\overline{12}$$.$$\overline{25}$$
9
______
6.5
3.25
3.25
______
0 $$\leftarrow$$ Remainder
$$\sqrt{12.25} = 3.5$$
What least number must be added to 700 to make the sum a perfect square? (Use Long division method).
Report Question
0%
25
0%
26
0%
28
0%
29
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Repeat the process till the remainder becomes zero
Divisor
$$\downarrow$$
Quotient
$$\downarrow$$
26
2
$$\overline{7}$$ $$\overline{00}$$
4
46
300
276
24$$\leftarrow$$ Remainder
We observe here $$26^2 < 700 < 27^2$$
The required number to be added = $$27^2 - 700$$
= 729 - 700
= 29
Therefore, 29 must be added to 700 to make it a perfect square.
State whether the statements are true (T) or false (F).
All numbers of a Pythagorean triplet are odd.
Report Question
0%
True
0%
False
Explanation
For Pythagorean triplet square of one should be equal to sum of square of other two.
Means, Pythagorean triplet as $$5^2 = 4^2 + 3^2$$
Here, 4 is an even number.
State whether the statements are true (T) or false (F).
The square root of 0.9 is 0.3.
Report Question
0%
True
0%
False
Explanation
The square of 0.3 = $$(0.3)^2 = 0.3 \times 0.3 = 0.09$$
Which least number must be subtracted to $$1025$$ to make a perfect square? (Use Long division method).
Report Question
0%
$$1$$
0%
$$2$$
0%
$$3$$
0%
$$4$$
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Repeat the process till the remainder becomes zero
Divisor
$$\downarrow$$
Quotient
$$\downarrow$$
$$32$$
$$3$$
$$\overline{10}$$ $$\overline{25}$$
$$9$$
$$62$$
$$125$$
$$124$$
$$1\leftarrow$$ Remainder
The remainder is 1. it represents that the square of $$32$$ is less than $$1025$$ by $$1$$.
Therefore, a perfect square will be obtained by subtracting $$1$$ from the given number $$1025$$.
So, perfect square $$= 1025 - 1$$
$$ = 1024$$
Find the square root of 67.24 using long division method.
Report Question
0%
8.2
0%
8.3
0%
8.1
0%
8.4
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Divisor
$$\downarrow$$
Quotient
$$\downarrow$$
8.2
8
$$\overline{67}$$.$$\overline{24}$$
64
______
1.62
3.24
3.24
______
0 $$\leftarrow$$ Remainder
$$\sqrt{67.24} = 8.2$$
Which least number must be subtracted to 899 to make a perfect square? (Use Long division method).
Report Question
0%
55
0%
56
0%
57
0%
58
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Repeat the process till the remainder becomes zero
Divisor
$$\downarrow$$
Quotient
$$\downarrow$$
29
2
$$\overline{8}$$ $$\overline{99}$$
4
49
499
441
58 $$\leftarrow$$ Remainder
The remainder is 58. it represents that the square of 29 is less than 899 by 58.
Therefore, a perfect square will be obtained by subtracting 58 from the given number 899.
So, perfect square = 899 - 58 = 841
Find the square root of 84.64 using long division method.
Report Question
0%
$$9.1$$
0%
$$9.2$$
0%
$$9.3$$
0%
$$9.4$$
A non-perfect square ends in 2, 3, 7 or ___.
Report Question
0%
4
0%
5
0%
0
0%
8
Explanation
A non-perfect square ends in 2, 3, 7 or 8.
Evaluate: $$\sqrt{10}$$ correct up to one place of decimal.
Report Question
0%
3.1
0%
3.16
0%
3.162
0%
3.1622
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Hence, $$\sqrt{10} = 3.1$$ (correct upto one decimal place)
Estimate the square root of $$500.$$
Report Question
0%
$$22.35$$
0%
$$20.3$$
0%
$$21.4$$
0%
$$23.6$$
Explanation
The two consecutive perfect squares among which $$500$$ lies are $$484(22^2)$$ and $$529(23^2)$$
So, the whole number part of the square root of $$500$$ is $$ 22.$$
The decimal part can be determined by the formula: $$\dfrac{\text{Given number – Smaller perfect square}}{ \text{Greater perfect square – smaller perfect square} }=\dfrac{500-484}{529-484}=\dfrac{16}{45}=0.35$$
So, the estimated value of the square root of $$500$$ by the approximation method is $$22.35.$$
What is the square root of 506.25 using long division method?
Report Question
0%
22.5
0%
21.4
0%
23.4
0%
25.3
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Divisor
$$\downarrow$$
Quotient
$$\downarrow$$
22.5
2
$$\overline{5}$$ $$\overline{06}$$.$$\overline{25}$$
4
_______
42
106
84
_______
44.5
22.25
22.25
_______
0
$$\leftarrow$$ Remainder
$$\sqrt{50.625} = 22.5$$
What is the square root of $$292.41$$ using long division method?
Report Question
0%
17.1
0%
17.2
0%
17.3
0%
17.4
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Hence, $$\sqrt{29.241} = 17.1$$
What is the square root of $$156.25$$ using long division method.
Report Question
0%
$$12.3$$
0%
$$12.5$$
0%
$$12.4$$
0%
$$12.7$$
Explanation
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Put the decimal point in the square root as soon as the integral part is exhausted.
8. Repeat the process till the remainder becomes zero.
Divisor
$$\downarrow$$
Quotient
$$\downarrow$$
12.5
1
$$\overline{1}$$ $$\overline{56}$$.$$\overline{25}$$
1
_______
22
56
44
_______
24.5
12.25
12.25
______
0
$$\leftarrow$$ Remainder
$$\sqrt{156.25} = 12.5$$
Estimate the value of $$\sqrt{750}$$.
Report Question
0%
24.3
0%
25.1
0%
23.2
0%
27.3
Explanation
$$27^2$$ = 729
$$28^2$$ = 784
In between this two squares, 750 is placed.
So average of $$\frac{27 + 28}{2}= 27.5$$
Then, $$27.5^2 = 756.25$$
So, $$\sqrt{750} \approx 27.3$$
Find the approximate value of $$\sqrt{5245}$$.
Report Question
0%
70.5
0%
72.3
0%
71.8
0%
79.2
Explanation
$$72^2$$ = 5184
$$73^2$$ = 5329
In between this two squares, 5245 is placed.
So average of $$\frac{72 + 73}{2}= 72.5$$
Then, $$72.5^2 = 5256.25$$
So, $$\sqrt{5245} \approx 72.3$$
What is an approximate value of $$\sqrt{9805}$$?
Report Question
0%
98.56
0%
97.23
0%
99.05
0%
100.34
Explanation
$$99^2$$ = 9801
$$100^2$$ = 10000
In between this two squares, 9805 is placed.
So the average of $$\frac{99 + 100}{2}= 99.5$$
Then, $$99.5^2 = 9900.25$$
So, $$\sqrt{9805} \approx 99.05$$
Find the approximate value of $$\sqrt{1235}$$.
Report Question
0%
$$35.15$$
0%
$$32.19$$
0%
$$30.25$$
0%
$$29.13$$
Explanation
$$35^2$$ = 1225
$$36^2$$ = 1296
In between this two squares, 1235 is placed.
So the average of $$\dfrac{35 + 36}{2}= 35.5$$
Then, $$35.5^2 = 1260.25$$
So $$\sqrt{1235}\approx35.15$$
What will be the units digit of the square of the given number $$5125$$?
Report Question
0%
$$0$$
0%
$$1$$
0%
$$5$$
0%
$$9$$
Explanation
Unit digit of multiplication of $$2$$ numbers is obtained by taking the last digit of the multiplication of two numbers in the unit place
Units digit of $$5125\times 5125$$ is obtained by taking the last digit of $$5\times 5=25$$
$$\Rightarrow $$ Unit digit of square of $$5125$$ is $$5$$.
What will be the unit's digit of the square of the given number $$297$$?
Report Question
0%
$$9$$
0%
$$7$$
0%
$$3$$
0%
$$1$$
Explanation
Unit's digit of multiplication of two numbers is obtained by taking the last digit of the multiplication of two numbers i.e. the digits at the unit place
Unit's digit of $$297×297$$ is obtained by taking the last digits i.e. $$7\times 7=49$$
$$\Rightarrow $$ Unit digit of square of $$297$$ is $$9$$.
The number of prime factors of $$36$$ is ____.
Report Question
0%
$$4$$
0%
$$3$$
0%
$$2$$
0%
$$1$$
Explanation
$$36=2\times2\times3\times3$$
Clearly, only 2 and 3 are prime factors of 36.
Option C is correct.
Estimate the square root of $$300$$.
Report Question
0%
$$12.44$$
0%
$$16.66$$
0%
$$17.32$$
0%
$$18.54$$
0:0:1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
0
Answered
0
Not Answered
0
Not Visited
Correct : 0
Incorrect : 0
Report Question
×
What's an issue?
Question is wrong
Answer is wrong
Other Reason
Want to elaborate a bit more? (optional)
Practice Class 8 Maths Quiz Questions and Answers
<
>
Support mcqexams.com by disabling your adblocker.
×
Please disable the adBlock and continue.
Thank you.
Reload page
