Question

Q1. Check wether √3 x √12 is a rational number or not.​

Answer 1

Answer:

it is a rational number...

$\sqrt{3} \times \sqrt{12} \\ = \sqrt{36} \\ = \sqrt{ {6}^{2} } \\ = 6$

therefore 6 is a answer..

and 6 is a rational number...

hope it helps u....

mark my answer to brainliest answer please....

Answer 2

Answer:

$\large\boxed{\sf{Rational\; Number}}$

Step-by-step explanation:

To check whether (√3 × √12) is rational or not.

We have given,

$\sqrt{3} \times \sqrt{12}$

But, we know that,

• $\sqrt{x} \times \sqrt{y} = \sqrt{xy}$

Therefore, we will get,

$= \sqrt{3 \times 12} \\ \\ = \sqrt{36}$

But, we know that,

• $36 = 6 \times 6$

Therefore, we will get,

$= \sqrt{6 \times 6}$

But, we know that,

• $x \times x = {x}^{2}$

Therefore, we will get,

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

But, we know that,

• $\sqrt{x} = {x}^{ \frac{1}{2} }$

Therefore, we will get,

$= {( {6}^{2}) }^{ \frac{1}{2} }$

But, we know that,

• ${( {x}^{m} )}^{n} = {x}^{mn}$

Therefore, we will get,

$= {6}^{(2 \times \frac{1}{2}) } \\ \\ = {6}^{1} \\ \\ = 6$

But, we know that 6 is a rational number.

Hence, (√3 × √12) is a rational number.