Is the simplified form of 2square root of 3 ⋅ 2square root of 6 rational?

Solution:

Given, 2 square root of 3 . 2 square root of 6

We have to find whether the simplified form of the given expression is rational or not.

2 square root of 3 can be written as 2√3

2 square root of 6 can be written as 2√6

The product is (2√3)(2√6)

= (2√3)(2√3.√2)

= 4(3√2)

= 12√2

Therefore, the simplified form 12√2 is irrational.

Example: Is the simplified form of 2 square root of 3 plus 3 square root of 3 rational?

Solution:

Given, 2 square root of 3 plus 3 square root of 3

We have to find whether the simplified form of the given expression is rational or not.

2 square root of 3 can be written as 2√3

3 square root of 6 can be written as 3√3

The product is 2√3 + 3√3

= √3(2 + 3)

= 5√3

Therefore, the simplified form is 5√3 and it is irrational.

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Is the simplified form of 2square root of 3 ⋅ 2square root of 6 rational?

Summary:

The simplified form of 2square root of 3 ⋅ 2square root of 6 is 12√2 and it is irrational.