Question

Which statement is true about the product square root of 2(3square root of 2 + square root of 14)?

It is rational and equal to 12.

It is rational and equal to 18.

It is irrational and equal to 6 + 2square root of 18.

It is irrational and equal to 3 +square root of 18.

Answer 1

It is rational and equal to 12.

Explanation:

Answer 2

`√(2) (3√(2) +√(14))=6+2√(7)`

Explanation:

Given :
`√(2) (3√(2) +√(14))`

Solution:

`√(2) (3√(2) +√(14))`

`3*2+√(28))`

`6+2√(7)`

Thus ,
`√(2) (3√(2) +√(14))=6+2√(7)`

Thus the solution is irrational since square root 7 does not have a perfect square and equal to 6+2square root of 14