Question

Find the square roots of the following numbers by prime factorization method.
$4096$

Answer 1

Given number is $4096$.

To find out,

The square root of the number using the prime factorization method.

We can represent $4096$ as a product of its prime factors as:

$4096=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

$\Rightarrow 4096=2^{12}$

$\Rightarrow 4096=(2^6{)}^2$

$\Rightarrow \sqrt{4096}=2^6$

$\Rightarrow \sqrt{4096}=2\times 2\times 2\times 2\times 2\times 2$

$=64$

Hence, the square root of $4096$ is $64$.