Question

find the square root of 576 in prime factorization method ​

Answer 1

Answer:

Step-by-step explanation:

a number calculated by squaring a number is known as a perfect square. For example, 16, 25, 576 etc are perfect squares. We can see 3 pairs of 2 and 1 pair of 3 in the above given prime factors of 576. Hence, the square root of 576 is 24.

Answer 2

Given:

Number 576

To find:

Square root by prime factorization.

Solution:

Let us find the prime factors of 576 first. The factors are as below:

$576=2*2*2*2*2*2*3*3$

Here, the prime factors of 576 are 2 and 3.

To find the square root, we consider a pair for each prime factors. Here, 2 is present in 3 pairs and 3 is present in 1 pair.

$\sqrt{576}=\sqrt{2*2*2*2*2*2*3*3}$

$\sqrt{576}=2*2*2*3$

$2*2*2*3=24$

$\sqrt{576}=24$

Hence, 24 is the square root of 576.

From this we can say that 576 is a perfect square because on multiplying 24 with 24 we get 576. When a number is multiplied with itself, it produces a perfect square.

The square root of 576 is 24 which is obtained by prime factorization