Question

subtract. write your answer in simplest form. $8\sqrt{2} - 4\sqrt{50}$

Explanation:

Step1: Simplify $\sqrt{50}$

We know that $50 = 25\times2$, so $\sqrt{50}=\sqrt{25\times2}$. By the property of square roots $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a = 25$, $b = 2$ and $a\geq0,b\geq0$), we have $\sqrt{25\times2}=\sqrt{25}\times\sqrt{2}=5\sqrt{2}$. Then $4\sqrt{50}=4\times5\sqrt{2}=20\sqrt{2}$.

Step2: Subtract the two terms

Now we have the expression $8\sqrt{2}-20\sqrt{2}$. Since both terms have the same radical part $\sqrt{2}$, we can combine them like like - terms. Using the distributive property $a\sqrt{c}-b\sqrt{c}=(a - b)\sqrt{c}$, here $a = 8$, $b = 20$, $c = 2$. So $8\sqrt{2}-20\sqrt{2}=(8 - 20)\sqrt{2}=- 12\sqrt{2}$.

Answer:

$-12\sqrt{2}$