Simplify - square root of r( square root of r-9 square root of s)

$- \sqrt{r} (\sqrt{r} - 9 \sqrt{s})$

Step 1

Apply the distributive property.

$- \sqrt{r} \sqrt{r} - \sqrt{r} (- 9 \sqrt{s})$

Step 2

Multiply $- \sqrt{r} \sqrt{r}$ .

Raise $\sqrt{r}$ to the power of $1$ .

$- ({\sqrt{r}}^{1} \sqrt{r}) - \sqrt{r} (- 9 \sqrt{s})$

Raise $\sqrt{r}$ to the power of $1$ .

$- ({\sqrt{r}}^{1} {\sqrt{r}}^{1}) - \sqrt{r} (- 9 \sqrt{s})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- {\sqrt{r}}^{1 + 1} - \sqrt{r} (- 9 \sqrt{s})$

Add $1$ and $1$ .

$- {\sqrt{r}}^{2} - \sqrt{r} (- 9 \sqrt{s})$

Step 3

Multiply $- \sqrt{r} (- 9 \sqrt{s})$ .

Multiply $- 9$ by $- 1$ .

$- {\sqrt{r}}^{2} + 9 \sqrt{r} \sqrt{s}$

Combine using the product rule for radicals.

$- {\sqrt{r}}^{2} + 9 \sqrt{s r}$

Step 4

Rewrite ${\sqrt{r}}^{2}$ as $r$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{r}$ as $r^{\frac{1}{2}}$ .

$- {(r^{\frac{1}{2}})}^{2} + 9 \sqrt{s r}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- r^{\frac{1}{2} \cdot 2} + 9 \sqrt{s r}$

Combine $\frac{1}{2}$ and $2$ .

$- r^{\frac{2}{2}} + 9 \sqrt{s r}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- r^{\frac{2}{2}} + 9 \sqrt{s r}$

Rewrite the expression.

$- r^{1} + 9 \sqrt{s r}$

Simplify.

$- r + 9 \sqrt{s r}$