Question

Find the smallest number by which 6912 should be divided so that the result is a perfect square. Pls show the steps

Answer 1

Prime factorization of 6912 = 2^8 * 3^3.

The prime factor 3 does not occur in pair.

In order to make it a perfect square, it must be divided by 3.

= > 6912 ÷ 3

= > 2304[48 * 48]

Which is a perfect square.

Therefore, the smallest number is 3.

Hope this helps!

Answer 2

Answer:

The smallest number is 3.

Step-by-step explanation:

Prime factorization of 6912 =  2x2x2x2x2x2x2x3x3x3 =$2^8 \times 3^3$.

On grouping the prime factors of  6912 we see that 3 is left out.

The prime factor 3 does not occur in pair.

Therefore, we must divide by 3 to obtain a perfect square.

 i.e.,   $\frac{6912}{3}$

        =2304

6912=2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

$\sqrt{6912}=2 \times 2 \times 2 \times 2 \times 3$

          = 48

It is a perfect square of 48.

Hence, the smallest number is 3 by which 6912 should be divided to get a perfect square.