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

The square root of

$\displaystyle\frac{36}{5}$ correct to two decimal places is _____________.

0%
$2.68$
0%
$2.69$
0%
$2.67$
0%
$2.66$

Explanation

We know

$\sqrt{\dfrac{36}{5}}=\dfrac {6}{\sqrt 5}$

$=\dfrac{6}{2.236}$ (Taking approximate value of square root

$\sqrt{5}$ )

$=2.6833$

Upto two decimal places:

$=2.68$

The number that must be subtracted from

$16161$ to get a perfect square is ________.

0%
$31$
0%
$32$
0%
$33$
0%
$34$

Explanation

Let the number is

$x$

Finding the square root of

$16161$

$\sqrt{16161}=127.1259$

Finding the square of

$127$

$127^2=16129$

$x=16161-16129$

$x=32$

Estiamate the square root of

$850$

0%
$29.15$
0%
$30.21$
0%
$98.23$
0%
$23.11$

Explanation

The square root of

$850$ is

$\sqrt {850}=\sqrt {25 \times 34}=5\sqrt {34}$

Square root of

$34$ lie between

$5$ and

$6$ .

square of

$5.5$ is

$30.25$

Now, we can say that square root of

$34$ lie between

$5.5$ and

$6$ .

Now, square of

$5.75$ is

$33.06$

So, square root of

$34$ lie between

$5.75$ and

$6$ .

Now, we have to choose the number

$5.85$

$(5.85)^2=34.225$ which is greater than

$34$ and close to

$34$

So, assume a number

$5.84$ .

$(5.84)^2=34.1056$

$(5.83)^2=33.9889$

Hence, we can say that square root of 34 lie between

$5.83$ and

$5.84$ .

So,

$5\times 5.83=29.15$ .

What approximate value will come in place of the question mark

$(?)$ in the following question? (you are not expected to calculate the exact value)

$\sqrt{8000}=?$

0%
$76$
0%
$89$
0%
$65$
0%
$97$
0%
$58$

Find the square root of

$225$ by division method.

0%
$5$
0%
$15$
0%
$25$
0%
$35$

State true (T) or false (F):
The square of 86 will have 6 at the units place.

0%
True
0%
False

Explanation

Digit at unit place of

$(86)^2 =$ Digit at the unit place of

$6^2 = 36$

Hence,

$6$ will be correct answer.

Write a Pythagorean triplet whose one number is 8

0%
$8,10,6$
0%
$15,10,5$
0%
$63,27,3$
0%
$80,40,20$

Explanation

$8^2=64$

$\Rightarrow$

$100-64=36$

$\Rightarrow$

$\sqrt{36}=6$

$\Rightarrow$

$\sqrt{100}=10$

Let

Hypotenuse

$=10$ [ Since its greater than

$6$ and

$8$ ]

Base

$=8$ and

Perpendicular

$=6$

$(Hypotenuse)^2=(Perpendicular)^2+(Base)^2$ [ Pythagoras theorem ]

$\Rightarrow$

$(10)^2=(6)^2+(8)^2$

$\Rightarrow$

$100=36+64$

$\Rightarrow$

$100=100$

$\therefore$ Pythagorean triplet are

$6,8,10$

What will be the unit digits of the square of the following numbers?

$39$ ,

$297$ ,

$5125$ ,

$7286$

0%
$9,9,1,6$
0%
$1,9,5,6$
0%
$9,2,5,2$
0%
$3,2,5,7$

Explanation

$(a)$ The numbers with unit's digits

$1$ or

$9$ has its square as

$1$

$\therefore\,$ the unit's digit of square of

$39$ is

$1$

$(b)$ The numbers with unit's digits

$3$ or

$7$ has its square as

$9$

$\therefore\,$ the unit's digit of square of

$297$ is

$9$

$(c)$ The numbers with unit's digits

$5$ has its square as

$5$

$\therefore\,$ the unit's digit of square of

$5125$ is

$5$

$(d)$ The numbers with unit's digits

$4$ or

$6$ has its square as

$6$

$\therefore\,$ the unit's digit of square of

$7286$ is

$6$

Use Pythagoras theorem to check which of following triplets would make a right triangle.

0%
$5, 20, 25$
0%
$7, 24, 25$
0%
$7, 23, 25$
0%
$15, 20, 25$

Explanation

The pythagoras theorem is

$a^2=b^2+c^2$

$20^2+5^2=425$ and

$25^2=625$

$25^2\neq20^2+5^2$

now check for b

$25^2=24^2+7^2$

$625=576+49$

$625=625$

so,

$25^2=24^2+7^2$

now check for c

$25^2=23^2+7^2$

$625=529+49$

$625\neq578$

Now ckeck for d

$25^2=20^2+15^2$

$625=400+225$

$625=625$

so only option

$B$ and

$D$ is correct.

Find the square root of

$126736$ by long division method.

0%
$355$
0%
$356$
0%
$366$
0%
$365$

Find the square root of which of the following numbers will be the least :

0%
$7\dfrac{58}{81}$
0%
$11\dfrac{14}{25}$
0%
$10\dfrac{1}{36}$
0%
$0.3481$

Explanation

$A.$

$7\dfrac{58}{81}=\dfrac{625}{81}$

$\Rightarrow$

$\sqrt{\dfrac{625}{81}}=\dfrac{25}{9}=2.77$

$B.$

$11\dfrac{14}{25}=\dfrac{289}{25}$

$\Rightarrow$

$\sqrt{\dfrac{289}{25}}=\dfrac{17}{5}=3.4$

$C.$

$10\dfrac{1}{36}=\dfrac{361}{36}$

$\Rightarrow$

$\sqrt{\dfrac{361}{36}}=\dfrac{19}{6}=3.16$

$D.$

$0.3481=\dfrac{3481}{10000}$

$\Rightarrow$

$\sqrt{\dfrac{3481}{10000}}=\dfrac{59}{100}=0.59$

$\therefore$ We can see,

$0.3481$ has least square root.

Find value of

$\sqrt{5184}$ .

0%
$72$
0%
$52$
0%
$82$
0%
$62$

Explanation

$\sqrt{5184}\\=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3}\\=\sqrt{2^6\times 3^4}\\=2^3\times3^2\\=8\times9=72$

Find the square root by prime factorisation:
i)

$196$
ii)

$225$

0%
$14, 25$
0%
$14, 15$
0%
$24, 15$
0%
$24, 25$

Explanation

(1)

$196=2\times 2\times 7\times 7$

$\sqrt{196}=\sqrt{2\times 2\times 7\times 7}$

$=\sqrt{2^{2}\times 7^{2}}$

$=2\times 7$

$=14$

(2)

$225=3\times 3\times 5\times 5$

$\sqrt{225}=\sqrt{3\times 3\times 5\times 5}$

$=\sqrt{3^{2}\times 5^{2}}$

$=3\times 5$

$=15$

Find the value of

$\sqrt{66049}$ .

0%
$253$
0%
$257$
0%
$347$
0%
$343$

Explanation

The number

$66049$ can only be divided by

$257$

$66049=257\times 257$

$66049=(257)^2$

$\sqrt{66049}=\sqrt{257^2}$

$\therefore$

$\sqrt{66049}=257$

What are the number which cannot come to the unit place of perfect square?

0%
$2$
0%
$3$
0%
$7$
0%
$8$

Explanation

Perfect square

$\rightarrow$ Unit place digit

$1^2=1$

$2^2=4$

$3^2=9$

$4^2=16$

$5^2=25$

$6^2=36$

$7^2=14$

$8^2=64$

$9^2=81$

$10^2=100$

We can see number which can comes to unit place of perfect squares are

$1,4,5,6,9$ and

$0$ .

$\therefore$ The numbers which can not come to the unit place of perfect square are

$2,3,7$ and

$8.$

A pythagorean triplet whose two numbers are 8 and 10, then third number is

0%
$6$
0%
$14$
0%
$16$
0%
$18$

Explanation

Require pythagorean triplet is (6,8,10) as

$6^2+8^2 = 36+64= 100 = 10^2$

Which of the following is a perfect square number?

0%
257
0%
256
0%
300
0%
None of these

Which of the following is pythagorean triplet?

0%
3 ,4 ,5
0%
5 ,12 ,13
0%
7 ,24 ,25
0%
All of these

Explanation

$\textbf{Step-Check option one by one using condition of pythagorian triplet}$

$\text{$$a,b$$ and $$c$$ are called pythagorean triplet if}$

$a^2+b^2=c^2$

$\text{Clearly,}$

$3^2+4^2=9+16=25=5^2$

$5^2+12^2=25+144=169=13^2$

$7^2+24^2=49+576=625=25^2$

$\text{Here all three of the given options are satisfy the pythagorean triplet.}$

$\textbf{Hence option D is correct}$

Find the atleast number which must be added to each of the following numbers to get a perfect square. Also find the square root of the perfect square numbers.

$a)525$

0%
4
0%
3
0%
1
0%
6
0%
12

Explanation

$i)\ 23^2=529$

$\therefore \$ it will add

$4$ to

$525$ we get

$529$

which is payout square

$\therefore \ 525+4=529=23^2$

$\therefore 4$ should be added

State whether the statements are true (T) or false (F).
For every natural number

$m, (2m - 1, 2m^2 - 2m, 2m^2 - 2m^2 + 1)$ is a Pythagorean triplet.

0%
True
0%
False

Explanation

$(2m- 1)^2 \neq (2m^3 - 2m )^2 + (2m^2 - 2m + 1)^2$
Or

$(2m^3 - 2m)^2 \neq (2m - 1)^2 + (2m^2 - 2m + 1)^2$
Or

$(2m^2 - 2m + 1)^2 \neq (2m -1 )^2 + (2m^3 - 2m )^2$

Which of the following is a Pythagorean triplet?

0%
$8, 6, 10$
0%
$8, 9, 10$
0%
$10, 12, 13$
0%
None of these

Explanation

"Pythagorean triples" are integer solutions to the Pythagorean Theorem,

$a^2 + b^2 = c^2.$

$A.$

$8,6,10$

$(Hypotenuse)^2=(Perpendicular)^2+(Base)^2$

$\Rightarrow$

$(10)^2=(8)^2+(6)^2$

$\Rightarrow$

$100=64+36$

$\Rightarrow$

$100=100$

$\therefore$

$8,6,10$ is a Pythagorean triplet

$B.$

$8,9,10$

$(Hypotenuse)^2=(Perpendicular)^2+(Base)^2$

$\Rightarrow$

$(10)^2=(8)^2+(9)^2$

$\Rightarrow$

$100=64+81$

$\Rightarrow$

$100\ne 146$

$\therefore$

$8,9,10$ is not a Pythagorean triplet

$C.$

$10,12,13$

$(Hypotenuse)^2=(Perpendicular)^2+(Base)^2$

$\Rightarrow$

$(13)^2=(10)^2+(12)^2$

$\Rightarrow$

$169=100+144$

$\Rightarrow$

$100\ne 244$

$\therefore$

$10,12,13$ is not a Pythagorean triplet

Find

$\sqrt {125}$ given

$\sqrt {5}=2.23607$

0%
$11.21$
0%
$11.38$
0%
$11.18$
0%
$11.24$

Explanation

$\sqrt{125}$

$=\sqrt{5\times 5\times 5}$

$=5\sqrt{5}$

$=5\times 2.23607$

$=11.180$ .

Which of the following numbers are not perfect square?

0%
2397
0%
121000
0%
25008
0%
19640
0%
All of above

Explanation

These all are

$not$ perfect square numbers because perfect square numbers always ends with

$(0,1,4,5,6,9)$ and if if last digit is

$0$ it should be even number of zeros.

Therefore all the given numbers are not perfect square.

Simplify :

$(64)^{1/2}$

0%
$12$
0%
$2$
0%
$8$
0%
$14$

Explanation

$(64)^{1/2}$

$=(8\times 8)^{1/2}$

$=(8^2)^{1/2}$

$=8^1$

$=8$ .

$\sqrt{2}=1.414$ then the value of

$\sqrt{8}$ is

0%
$2.828$
0%
$1.828$
0%
$2.282$
0%
$2.288$

Explanation

$\sqrt{2}=1.414$ (given)

$\sqrt{8}=\sqrt{2\times 2\times 2}=2\sqrt{2}=2\times 1.414=2.828$

$\therefore \sqrt{8}=2.828$

Square root of 169 is

0%
13
0%
14
0%
15
0%
None of these

Find which of the square of the following numbers are even ?

0%
$431$
0%
$2826$
0%
$7779$
0%
$82004$

Explanation

We know that square of an odd number is odd and square of an even number is even

$(i)$ The square of

$431$ is an odd number

$\because 431$ is an odd number.

$(ii)$ The square of

$2826$ is an even number

$\because 2826$ is an even number.

$(iii)$ The square of

$7779$ is an odd number

$\because 7779$ is an odd number.

$(iv)$ The square of

$82004$ is an even number

$\because 82004$ is an even number.

Mark the correct alternative of the following.
Which of the following is/are not Pythagorean triplet(s)?

0%
$3, 4, 5$
0%
$8, 15, 17$
0%
$7, 24, 25$
0%
$13, 26, 29$

Explanation

We have to check for pythagorean triplets.

Option (A)

$3, 4, 5$

It is easy to check that

$3^2 + 4^2 = 5^2$

$25 = 25$

$3, 4, 5$ is pythagorean triplet.

Option (B)

$8 , 15 , 17$

Observe that

$8^2 + 15^2 = 64 + 225$

$= 289$

$= 17^2$

Hence

$8, 15, 17$ is pythagorean triplet

Option (C)

$7, 24, 25$

observe that

$7^2 + 24^2 = 49 + 576$

$= 625$

$= 25^2$

$7, 24, 25$ is pythagorean triplet.

Option (D)

$13, 26, 29$

check that

$13^2 + 26^2 = 169 + 676$

$= 845$

and

$29^2 = 841$

$13^2 + 26^2 \neq 29^2$

Hence option D is correct.

Which of the following number is not a perfect square?

0%
$1444$
0%
$3136$
0%
$961$
0%
$2222$

Explanation

Explanation: According to the property of square, a number ending with

$2,3,7$ and

$8$ is not a perfect square.

Hence,

$2222$ is not a perfect square.

Which of the following cannot be the unit digit of a perfect square number?

0%
$6$
0%
$1$
0%
$9$
0%
$8$

Explanation

As we know that all the perfect square number ends with

$1,4,9,6,5,00$
Hence, D will be correct answer.

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

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Practice Class 8 Maths Quiz Questions and Answers

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