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.

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.

geerky42 · Answer

$$\sqrt{2}(3\sqrt2 + \sqrt{14})$$Right?

What do you think so far?

geerky42 · Answer

You can split $\sqrt{14}$ into two square roots;

$\sqrt{14} = \sqrt{2\cdot7}=\sqrt2\sqrt7$

geerky42 · Answer

$$\sqrt{2}(3\sqrt2 + \sqrt2\sqrt7)$$

Now distribute $\sqrt2$

anonymous · Answer

Um I think I get it but what next?

anonymous · Answer

simplifying further, you'll get $$6+2\sqrt{7}$$

anonymous · Answer

so would that be c ? @aryandecoolest

anonymous · Answer

@geerky42

anonymous · Answer

C