Finding Square Root through Prime Factorisation

Q. For $2028$ 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.
[4 marks]
[NCERT - Ex 6.3, Q5 (iv)]
[Finding Square Root]

Q.

Square root of 256 is __.

Q.

Which number should be multiplied to 1575 to make it a square number?

1. 4

2. 5

3. 6

4. 7

Q.

Use Prime Factorization method to find the square root of the following:-

$i.\sqrt{\left(1024\right)}$ = ______

$ii.\sqrt{\left(2025\right)}$ = _______

1. 32, 45

2. 28, 25
3. 28, 45

4. 36, 35

Q.

Three identical square sheets of paper need to be cut into 4, 5, and 6 stripes of equal size respectively. Find the minimum length of the side of the original square sheet.

1. 45

2. 40

3. 30

4. 25

Q.

Square root of 1024 is 32.

1. True
2. False

Q.

1, 024 trees are planted in a grid fashion such that the number of rows is equal to the number of columns. One row and one column of trees are cut such that the number of rows and columns after cutting remain equal. Find the number of trees that were cut?

1. 63

2. 65

3. 67

4. 61

Q.

Simplify
$\sqrt{\sqrt{81}}$ =

1. 27

2. 9

3. 3

4. Can't be determined

Q. What is the value of $\sqrt{99}\times \sqrt{396}$?

1. 208
2. 198
3. None of these
4. 254

Q. Simplify:
$4\sqrt{3}(2\sqrt{27}-4\sqrt{48})-5\sqrt{3}(\sqrt{12}-3\sqrt{75})$.

1. 75
2. 48
3. 78
4. 57