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, 45
• B. 36, 35
• C. 28, 25
• D. 28, 45

Answer 1

The correct option is A

32, 45

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

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