Question

add. write your answer in simplest form.
$-9sqrt{63} + 7sqrt{7}$

Explanation:

Step1: Simplify $\sqrt{63}$

We know that $63 = 9\times7$, so $\sqrt{63}=\sqrt{9\times7}$. By the property of square roots $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a = 9$, $b = 7$ and $a\geq0,b\geq0$), we have $\sqrt{9\times7}=\sqrt{9}\times\sqrt{7}=3\sqrt{7}$. Then $- 9\sqrt{63}=-9\times3\sqrt{7}=-27\sqrt{7}$.

Step2: Combine like terms

Now we have the expression $-27\sqrt{7}+7\sqrt{7}$. Since both terms have $\sqrt{7}$, we can combine the coefficients: $(-27 + 7)\sqrt{7}=-20\sqrt{7}$.

Answer:

$-20\sqrt{7}$