Finding Square Root through Prime Factorisation

Q.

Find the square root of $9216$ by the Prime Factorisation method.

Q. Find the square root of:
(i) 0.0169
(ii) $96\frac{1}{25}$

Q. $\text{Find the value of}\sqrt{248+\sqrt{52+\sqrt{144}}}.$

1. 13
2. 12
3. 14
4. 16

Q. Find the square root of 256.

1. 16
2. 14
3. 18
4. 22

Q.

Find the square root of 2025 by prime factorisation.

1. 25

2. 35

3. 50

4. 45

Q.

Q.

Which of the following cant be the units digit in a perfect square number?

Q.

What is the smallest number by which 2592 must be multiplied so that the product is a perfect square?

1. 7

2. 5

3. 3

4. 2

Q. The square root of $3^0+3^1+3^2+3^3+3^4$ is

1. $11$
2. $3^2$
3. $13$
4. $3^0$

Q. What must be added to 14360 so that the number becomes a perfect square?

1. 40

Q.

Evaluate:

$\sqrt{5(2\frac{3}{4}-\frac{3}{10})}$

1. $2\frac{3}{2}$

2. $1\frac{5}{2}$

3. $4\frac{1}{2}$

4. $3\frac{1}{2}$

Q. Q8) Express each of the following as product of powers of prime factors:
(a) 81 ×128 (b) 256 × 121

Q. Find the square root of the following number by the prime factorisation method.
$\frac{5625}{3969}$

Q.

What is the value of $\sqrt[3]{38}+\frac{1}{\sqrt[3]{38}}$ ?

1. 1

2. 2.5

3. 2

4. 0.5

Q. Which of the following cannot be a perfect square?

1. 256
2. 682
3. 625
4. 72398
5. 4000
6. 27
7. 529
8. 5143

Q. What is the square root of $63$ in simplest radical form?

Q. Value of $\sqrt[3]{3392}\times \sqrt[3]{3448}$ is ______.

1. 54
2. 56
3. 50
4. 52

Q. Read out each of the following numbers carefully and specify the natural numbers in it:
$87,54,0,-13,-4.7,\sqrt{7},217,\sqrt{15},-87,3\sqrt{7},4.807,0.002,\sqrt{16}$ and $2+\sqrt{3}.$

1. $87,54,$ $\sqrt{16}$, $217$
2. $0,-13,-4,7,217,54,87$
3. $\sqrt{7}$, $\sqrt{15}$, $3\sqrt{7}$, $\sqrt{16}$, $2+\sqrt{3}$,
4. $0,87,54,\sqrt{16}$

Q. how to find the square root of 131??

Q. There are ______ non-square natural numbers between the square of 11 and the square of 12.

1. 24
2. 22
3. 21
4. 23

Q. There are natural numbers between $17^2$ and $18^2$

Q. Find the value of $(2p\times 3p^2)-(3p^5\times \frac{2}{p^2})$

1. $0$
2. $2p^3$
3. $3p^3$
4. $3p^4$

Q. Evaluate : $2550-[510-(270-(90-\overline{80+7})\left)\right]$.
(4 Marks)

Q. Find the smallest positive number from the numbers below

1. $10-3\sqrt{11}$
2. $51-10\sqrt{26}$
3. $18-5\sqrt{13}$
4. $3\sqrt{11}-10$

Q. Evaluate 34 × 43 using suitable property. ​

Q. Which of the following is a square of an even number?

1. 144
2. 441
3. 169
4. 625

Q. Compare the following pair of surd.
$5\sqrt{5},7\sqrt{2}$

Q. $\sqrt[3]{3\frac{250}{2000}}+\sqrt[3]{3\frac{6750}{2000}}+\frac{\sqrt[3]{327}}{2}$

Q. Find the square roots of 1764 by the Prime Factorization Method.

Q. Evaluate:
$2550-[510-\{270-(90-\overline{80+7}\left)\right\}]$