Question

Is the simplified form of 2square root of 3 • square root of 12 rational?. Yes. No

Answer 1

Answer:

Yes, the simplified form of the given radical expression is rational.

Step-by-step explanation:

We are asked to determine whether the simplified form of $2\sqrt{3} \cdot \sqrt{12}$ is rational or not.

To solve our given problem we will use exponent property for radicals $a\sqrt{m}\cdot\sqrt{n}=a\sqrt{m\cdot n}$.

$2\sqrt{3} \cdot \sqrt{12}=2\sqrt{3\cdot 12}$

$2\sqrt{3} \cdot \sqrt{12}=2\sqrt{36}$

$2\sqrt{3} \cdot \sqrt{12}=2*6$

$2\sqrt{3} \cdot \sqrt{12}=12$

Since our given radical expression simplifies to a rational, therefore, our answer is yes.

Answer 2

The product asked above may be given expressed by the expression,
                         (2) x (sqrt 3) times (sqrt 12)
Two is also equivalent to sqrt of 4. The operation may be expressed as,
                                   (sqrt 4) x (sqrt 3) x sqrt (12)
The product is sqrt (144). This gives an answer of 12 and it is rational.