Question

Use prime factors to explain why 6 x 54 is a perfect square

Answer 1

Answer:

Step-by-step explanation:

6×54=2×3×2×3×3×3=2²×3²××3²=(2×3×3)²= perfect square

Answer 2

Answer:

The explanation is given below.

Step-by-step explanation:

Given 6 x 54

We will write the prime factors of 6 x 54

First of all, calculating the prime factors of 6

=> 6 = 2 x 3

Then, we will calculate the prime factors of 54

=> 54 = 2 x 3 x 3 x 3

Therefore, 6 x 54 = 2 x 3 x 2 x 3 x 3 x 3

                             = 2 x 2 x 3 x 3 x 3 x 3

As we need to find the perfect square,

We will pair the factors in pair of two.

=> 6 x 54 = (2 x 2) x (3 x 3) x (3 x 3)

                = 2² x 3² x 3²

                = (2 x 3 x 3)²

                = 18²

We can also verify as 6 x 54 = 324  and $\sqrt{324}$ = 18

Hence Verified.