Finding Square Roots Using Prime Factorisation

Q.

Find the square root of the number correct to two decimal places

2

Q.

Find by prime factorization the square of 9025 (show complete solution)

Q.

The square root of 99 is(approximated to 2 decimal digits) _____ .

1. 9.90

2. 9.95

3. 9.86

4. 9.85

Q. Find the square root of 82.6 correct to two places of decimal.

Q.

Find the smallest square number which can be divisible by 4, 12 and, 16.

Q.

Find the square root of $237.615$ correct to the three places of decimals.

Q.

By which number, 588 be multiplied so as to get a perfect square?

1. 3

2. 5

3. 7

4. 2

Q.

The square root of a number whose prime factorisation is

2 x 2 x 3 x 3 x 3 x 3 x 5 x 5 is:

1. 80

2. 90

3. 180

4. 45

Q.

Find the square root of 5893.27 correct to 2 decimal places

Q. Find the square root of 245 correct to two places of decimal.

Q.

Question 3 (iii)
Find the square root of the following decimal numbers:
51.84

Q. Fin the square root of 96.04

Q. How to find square root of 768 by prime factorisation

Q.

Find the smallest number by which 7623 must be divided to get a perfect square.

1. 9

2. 7

3. 3

4. 5

Q.

Question 3 (i)
Find the square root of the following decimal numbers:
2.56

Q.

From which number should 867 be multiplied to get a perfect square

Q.

Question 98

Solve the following question:

Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.

Q.

Find the largest perfect square factor of each of the following numbers:

(i) 48; (ii) 11280; (iii) 729; (iv) 1352.

Q.

Find the smallest number by which 405 must be divided, so as to get a perfect square.

1. 3

2. 9

3. 15

4. 5

Q. Evaluate the square root of 20.25.

1. 2.5
2. 3.5
3. 4.5
4. 5.5

Q.

For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.

(i) 252 (ii) 180

(iii) 1008 (iv) 2028

(v) 1458 (vi) 768

Q.

Question 6
Find the length of the side of a square whose area is $441m^2$?

Q. Find the least square number which is exactly divisible by each of the numbers 8, 12, 15 and 20.

Q.

Find the square root of the following decimal numbers by division method

5.774409

Q.

Question 63

State whether the following statement is true or false:

1000 is a perfect square.

Q.

Question 1 (iii)
What could be the possible ‘one’s’ digits of the square root of each of the following numbers:

998001

Q. Using the prime factorisation method, find which of the following numbers are perfect squares:
(i) 441
(ii) 576
(iii) 11025
(iv) 1176
(v) 5625
(vi) 9075
(vii) 4225
(viii) 1089

Q.

Question 1 (ii)
What could be the possible ‘one’s’ digit of the square root of following number:

99856

Q. Find square root of 86.71 correct up to two decimal places

Q. Approximate value of square root of 5 up to the 2nd decimal place?

1. 2.236
2. 2.449
3. 2.25
4. 2.24