Question

Is the simplified form of 2square root of 3 + 3square root of 3 rational?

Answer 1

`2\sqrt3+3\sqrt3=(2+3)\sqrt3=\boxed{5\sqrt3}\in\mathbb{R}\\\\It's\ not\ rational.`

Answer 2

No, the simplified form is not rational.

Explanation:

We have been given the expression
`2\sqrt3+3\sqrt3`

We can easily simplify this expression by adding the terms. We can add the terms because both have the same radical.

On adding, we get

`2\sqrt3+3\sqrt3=5\sqrt3`

Now, we know that
`\sqrt3` is an irrational number. Now, we know that the product of rational and irrational is irrational . Hence, when we multiply a rational number 5 with irrational number
`\sqrt3` then the result would be irrational.

Hence, the simplified form is irrational