Question

Prove that the product of two perfect squares is also a perfect square.

Answer 1

Hey mate !!

Here's your answer !!

According to the law of exponents, it says that:

When two numbers of equal powers and different bases are multiplied, the bases get multiplied with a common whole power. That is:

a² × b² = ( ab )²

So the product of two perfect squares is always a perfect square since the powers are same which is 2.

Example : ( 3 )² × ( 7 )² = ( 3 × 7 ) ² = (21)² = 441

Verification : 9 × 49 = 441

Hence proved !!

Hope it helps !!

Cheers !! 

Answer 2

Hey friend, Harish here.

Here is your answer:

To prove,

The product of two perfect square is also a perfect square.

Proof,

Let the perfect squares be :  a² & b².

We know that,  xⁿ × yⁿ = (x × y)ⁿ = (xy)ⁿ.

Here, n =2, & x = a , y =b.

Then,  a² × b² = (a × b)² = (ab)²

We know that, (ab)² is also a perfect square.

Verify:

Let a= 2  & b = 4.

Then, a² = 4 &  b² = 16.

So, a² × b² = 4 × 16 = 64.

We know that, 64 = 8² . Which is also a perfect square.

Hence we proved that, product of two perfect squares is also a perfect square.
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Hope my answer is helpful to you.