Question

subtract. write your answer in simplest form.
$-6sqrt{98} - 10sqrt{2}$

Explanation:

Step1: Simplify $\sqrt{98}$

We know that $98 = 49\times2$, so $\sqrt{98}=\sqrt{49\times2}$. By the property of square roots $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a = 49$, $b = 2$ and $a\geq0,b\geq0$), we have $\sqrt{49\times2}=\sqrt{49}\times\sqrt{2}=7\sqrt{2}$.

Step2: Substitute back into the original expression

The original expression is $-6\sqrt{98}-10\sqrt{2}$. Substituting $\sqrt{98} = 7\sqrt{2}$, we get $-6\times7\sqrt{2}-10\sqrt{2}$.

Step3: Calculate $-6\times7\sqrt{2}$

$-6\times7\sqrt{2}=-42\sqrt{2}$. So the expression becomes $-42\sqrt{2}-10\sqrt{2}$.

Step4: Combine like terms

Since both terms have $\sqrt{2}$, we can combine them. Using the distributive property $ac + bc=(a + b)c$, here $a=-42$, $b = - 10$ and $c=\sqrt{2}$. So $-42\sqrt{2}-10\sqrt{2}=(-42 - 10)\sqrt{2}=-52\sqrt{2}$.

Answer:

$-52\sqrt{2}$