Question

What is the simplest form of the radical expression 3 sqrt 24 - 2 sqrt 54 + 2 sqrt 18

Please show all of your work.

Answer 1

Answer:

$6\sqrt{2}$

Step-by-step explanation:

we have

$3\sqrt{24} -2\sqrt{54}+2\sqrt{18}$

we know that

$\sqrt{24}=\sqrt{2^{3}3}=2\sqrt{6}$

$\sqrt{54}=\sqrt{3^{3}2}=3\sqrt{6}$

$\sqrt{18}=\sqrt{3^{2}2}=3\sqrt{2}$

Substitute

$3(2\sqrt{6}) -2(3\sqrt{6})+2(3\sqrt{2})$

$(6\sqrt{6}) -(6\sqrt{6})+(6\sqrt{2})$

$6\sqrt{2}$