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

Answer:

$\sqrt{2} (3\sqrt{2} +\sqrt{14})=6+2\sqrt{7}$

Step-by-step explanation:

Given : $\sqrt{2} (3\sqrt{2} +\sqrt{14})$

Solution:

$\sqrt{2} (3\sqrt{2} +\sqrt{14})$

$3*2+\sqrt{28})$

$6+2\sqrt{7}$

Thus ,  $\sqrt{2} (3\sqrt{2} +\sqrt{14})=6+2\sqrt{7}$

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

Answer 2

Answer:

It is rational and equal to 12.

Step-by-step explanation: