Question

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

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

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

• A. 32
• B. 45
• C. 28, 25
• D. 32, 25

Answer 1

The correct option is A

32

i. $1024=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=2^2\times 2^2\times 2^2\times 2^2\times 2^2\sqrt{\left(1024\right)}=\sqrt{(2^2\times 2^2\times 2^2\times 2^2\times 2^2)}=\sqrt{(2\times 2\times 2\times 2\times 2{)}^2}=2\times 2\times 2\times 2\times 2=32$

ii. $2025=3\times 3\times 3\times 3\times 5\times 5=3^2\times 3^2\times 5^2\sqrt{\left(2025\right)}=\sqrt{(3^2\times 3^2\times 5^2)}=\sqrt{(3\times 3\times 5{)}^2}=3\times 3\times 5=45$