Question

What is 2√20 - 4√45 + 7√12 in simplest radical form? Show your work!

Answer 1

Answer:

$14\sqrt{3}-8\sqrt{5}$

Step-by-step explanation:

we have

$2\sqrt{20}-4\sqrt{45}+7\sqrt{12}$

we know that

$2\sqrt{20}=2\sqrt{2^{2}5} =2(2)\sqrt{5}=4\sqrt{5}$

$4\sqrt{45}=4\sqrt{3^{2}5} =4(3)\sqrt{5}=12\sqrt{5}$

$7\sqrt{12}=7\sqrt{2^{2}3} =7(2)\sqrt{3}=14\sqrt{3}$

substitute the values in the expression above

$4\sqrt{5}-12\sqrt{5}+14\sqrt{3}$

Combine like terms

$14\sqrt{3}-8\sqrt{5}$