Simplify - square root of a( square root of a-9 square root of b)

$- \sqrt{a} (\sqrt{a} - 9 \sqrt{b})$

Step 1

Apply the distributive property.

$- \sqrt{a} \sqrt{a} - \sqrt{a} (- 9 \sqrt{b})$

Step 2

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

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

$- ({\sqrt{a}}^{1} \sqrt{a}) - \sqrt{a} (- 9 \sqrt{b})$

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

$- ({\sqrt{a}}^{1} {\sqrt{a}}^{1}) - \sqrt{a} (- 9 \sqrt{b})$

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

$- {\sqrt{a}}^{1 + 1} - \sqrt{a} (- 9 \sqrt{b})$

Add $1$ and $1$ .

$- {\sqrt{a}}^{2} - \sqrt{a} (- 9 \sqrt{b})$

Step 3

Multiply $- \sqrt{a} (- 9 \sqrt{b})$ .

Multiply $- 9$ by $- 1$ .

$- {\sqrt{a}}^{2} + 9 \sqrt{a} \sqrt{b}$

Combine using the product rule for radicals.

$- {\sqrt{a}}^{2} + 9 \sqrt{b a}$

Step 4

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

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

$- {(a^{\frac{1}{2}})}^{2} + 9 \sqrt{b a}$

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

$- a^{\frac{1}{2} \cdot 2} + 9 \sqrt{b a}$

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

$- a^{\frac{2}{2}} + 9 \sqrt{b a}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- a^{\frac{2}{2}} + 9 \sqrt{b a}$

Rewrite the expression.

$- a^{1} + 9 \sqrt{b a}$

Simplify.

$- a + 9 \sqrt{b a}$