Square Root by Prime Factorization

Q. By what least number should the given number be divided to get a perfect square number? In each case, find the number whose square is the new number.
(i) 1575
(ii) 9075
(iii) 4851
(iv) 3380
(v) 4500
(vi) 7776
(vii) 8820
(viii) 4056

Q. Find the least number which is a perfect square and which is also divisible by 12, 15
and 24.

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

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

Q.

The least number by which 125 must be divided to make it a perfect square is

1. 5

2. 3

3. 15

4. 25

Q. Which is the smallest number that has to be multiplied to make 1620 a perfect square?

1. 3
2. 5
3. 7
4. 2

Q.

Find the smallest number by which 9408 must be divided, so that quotient is a perfect square. Find the square root of the quotient?

Q.

The least number by which 425 must be multiplied to make it a perfect square is

1. 3

2. 15

3. 17

4. 5

Q. In the square root of 1296, what would be the highest power of 3 ?

1. 0
2. 4
3. 1
4. 2

Q.

Find the smallest square number that is divisible by each of the numbers $4,9$ and $10$.

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 smallest positive integer with which one has to multiply each of the following numbers to get a perfect square:

(i) 847; (ii) 450; (iii) 1445; (iv) 1352.

Q.

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

(i) $252$ (ii) $2925$ (iii) $396$ (iv) $2645$ (v) $2800$ (vi) $1620$

Q. By what least number should the given number be multiplied to get a perfect square number? In each case, find the number whose square is the new number.
(i) 3975
(ii) 2156
(iii) 3332
(iv) 2925
(v) 9075
(vi) 7623
(vii) 3380
(viii) 2475

Q. Find the least square number which is exactly divisible by each of the numbers 6, 9, 15 and 20.

Q.

Find the smallest number by which 180 must be multiplied so that the product is perfect square.

Q. Find the smallest number by which 10368 be divided so that the result is a perfect square also find the square root of resulting number

Q. Find the least square number which is exactly divisible by each of the numbers 6, 9, 15 and 20.

Q. should be multiplied to 1575 to make it a square number.

1. 4
2. 5
3. 6
4. 7

Q. The length of the side of a square with an area of $1600m^2$ is ____.

1. 80m
2. 44m
3. 30m
4. 40m

Q.

Find the smallest square number that is divisible by each of the numbers 4, 9, and 10.

Q.

Find the smallest number by which 243 should be multiplied to get perfect square.

1. 3

2. 4

3. 1

4. 2

Q.

What is the least perfect square which leaves the remainder 1 when divided by 7 as well as by 11?

Q.

Find the smallest square number that is divisible by each of the numbers 4, 9, and 10.

Q. Find the smallest number by which 252 must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained.

Q. Find the smallest number by which 3645 must be divided so that it becomes a perfect square. Also, find the square root of the resulting number.

Q. Match the following.

1. 26
2. 32
3. 22
4. 25

Q. Square root of 256 is

1. 18
2. 16
3. 14
4. 24

Q. Fill in the blanks.
(i) 1 + 3 + 5 + 7 + 9 + 11 + 13 = (.........)².
(ii) $\sqrt{1681}=.........$
(iii) The smallest square number exactly divisible by 2, 4, 6 is .........
(iv) A given number is a perfect square having n digits, where n is odd. Then, its square root will have ......... digits.

Q.

A teacher wants to arrange 2800 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 96 were left out after the arrangement.

1. 52

2. 56

3. 54

4. 58

Q. Find square root of 45 * square root of 20 by prime factorisation method