Question

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

Answer 1

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

Explanation:

We are asked to determine whether the simplified form of
`2√(3) \cdot √(12)` is rational or not.

To solve our given problem we will use exponent property for radicals
`a√(m)\cdot√(n)=a√(m\cdot n)`.

`2√(3) \cdot √(12)=2√(3\cdot 12)`

`2√(3) \cdot √(12)=2√(36)`

`2√(3) \cdot √(12)=2*6`

`2√(3) \cdot √(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.