Question

simplify. 8\sqrt{200}-3\sqrt{162} enter your answer, in simplest radical form, in the box.

Explanation:

Step1: Simplify $\sqrt{200}$

We know that $200 = 100\times2$, so $\sqrt{200}=\sqrt{100\times2}=\sqrt{100}\times\sqrt{2}=10\sqrt{2}$. Then $8\sqrt{200}=8\times10\sqrt{2} = 80\sqrt{2}$.

Step2: Simplify $\sqrt{162}$

We have $162=81\times2$, so $\sqrt{162}=\sqrt{81\times2}=\sqrt{81}\times\sqrt{2}=9\sqrt{2}$. Then $3\sqrt{162}=3\times9\sqrt{2}=27\sqrt{2}$.

Step3: Subtract the two simplified terms

$8\sqrt{200}-3\sqrt{162}=80\sqrt{2}-27\sqrt{2}=(80 - 27)\sqrt{2}=53\sqrt{2}$.

Answer:

$53\sqrt{2}$