MCQ Questions for Class 8 Maths Squares And Square Roots Quiz 7

Find the value of

$\sqrt {25}$ .

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.

0%
True
0%
False

Explanation

$\because (7)^2 = 49$ ends in 9 and

$(7)^3 = 343$ does not ends in 7.

Estimate:

$\sqrt { 60 }$

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

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?

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.

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

$20$ ?

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).

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.

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).

0%
25
0%
26
0%
28
0%
29

Explanation

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.

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.

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).

0%
$1$
0%
$2$
0%
$3$
0%
$4$

Explanation

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.

0%
8.2
0%
8.3
0%
8.1
0%
8.4

Explanation

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).

0%
55
0%
56
0%
57
0%
58

Explanation

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.

0%
$9.1$
0%
$9.2$
0%
$9.3$
0%
$9.4$

A non-perfect square ends in 2, 3, 7 or ___.

0%
4
0%
5
0%
0
0%
8

Evaluate:

$\sqrt{10}$ correct up to one place of decimal.

0%
3.1
0%
3.16
0%
3.162
0%
3.1622

Explanation

Hence,

$\sqrt{10} = 3.1$ (correct upto one decimal place)

Estimate the square root of

$500.$

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?

0%
22.5
0%
21.4
0%
23.4
0%
25.3

Explanation

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?

0%
17.1
0%
17.2
0%
17.3
0%
17.4

Explanation

Hence,

$\sqrt{29.241} = 17.1$

What is the square root of

$156.25$ using long division method.

0%
$12.3$
0%
$12.5$
0%
$12.4$
0%
$12.7$

Explanation

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

$\sqrt{750}$ .

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

$\sqrt{5245}$ .

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

$\sqrt{9805}$ ?

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

$\sqrt{1235}$ .

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,

$35.5^2 = 1260.25$

$\sqrt{1235}\approx35.15$

What will be the units digit of the square of the given number

$5125$ ?

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

$297$ ?

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 ____.

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

$300$ .

0%
$12.44$
0%
$16.66$
0%
$17.32$
0%
$18.54$

CBSE Questions for Class 8 Maths Squares And Square Roots Quiz 7 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

CBSE Questions for Class 8 Maths Squares And Square Roots Quiz 7 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

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