Basic Math Examples

$\sqrt{16 a} - \sqrt{a b^{4}} \div \sqrt{4 a} + \sqrt{a b^{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $16 a$ as ${(2^{2})}^{2} a$ .

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Step 1.1.1

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} a} - \sqrt{a b^{4}} \div \sqrt{4 a} + \sqrt{a b^{2}}$

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{{(2^{2})}^{2} a} - \sqrt{a b^{4}} \div \sqrt{4 a} + \sqrt{a b^{2}}$

Step 1.2

Pull terms out from under the radical.

$2^{2} \sqrt{a} - \sqrt{a b^{4}} \div \sqrt{4 a} + \sqrt{a b^{2}}$

Step 1.3

Raise $2$ to the power of $2$ .

$4 \sqrt{a} - \sqrt{a b^{4}} \div \sqrt{4 a} + \sqrt{a b^{2}}$

Step 1.4

Rewrite the division as a fraction.

$4 \sqrt{a} - \frac{\sqrt{a b^{4}}}{\sqrt{4 a}} + \sqrt{a b^{2}}$

Step 1.5

Combine $\sqrt{a b^{4}}$ and $\sqrt{4 a}$ into a single radical.

$4 \sqrt{a} - \sqrt{\frac{a b^{4}}{4 a}} + \sqrt{a b^{2}}$

Step 1.6

Reduce the expression $\frac{a b^{4}}{4 a}$ by cancelling the common factors.

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Step 1.6.1

Cancel the common factor.

$4 \sqrt{a} - \sqrt{\frac{a b^{4}}{4 a}} + \sqrt{a b^{2}}$

Step 1.6.2

Rewrite the expression.

$4 \sqrt{a} - \sqrt{\frac{b^{4}}{4}} + \sqrt{a b^{2}}$

Step 1.7

Rewrite $b^{4}$ as ${(b^{2})}^{2}$ .

$4 \sqrt{a} - \sqrt{\frac{{(b^{2})}^{2}}{4}} + \sqrt{a b^{2}}$

Step 1.8

Rewrite $4$ as $2^{2}$ .

$4 \sqrt{a} - \sqrt{\frac{{(b^{2})}^{2}}{2^{2}}} + \sqrt{a b^{2}}$

Step 1.9

Rewrite $\frac{{(b^{2})}^{2}}{2^{2}}$ as ${(\frac{b^{2}}{2})}^{2}$ .

$4 \sqrt{a} - \sqrt{{(\frac{b^{2}}{2})}^{2}} + \sqrt{a b^{2}}$

Step 1.10

Pull terms out from under the radical, assuming positive real numbers.

$4 \sqrt{a} - \frac{b^{2}}{2} + \sqrt{a b^{2}}$

Step 1.11

Reorder $a$ and $b^{2}$ .

$4 \sqrt{a} - \frac{b^{2}}{2} + \sqrt{b^{2} a}$

Step 1.12

Pull terms out from under the radical.

$4 \sqrt{a} - \frac{b^{2}}{2} + b \sqrt{a}$

Step 2

Move $4 \sqrt{a}$ .

$- \frac{b^{2}}{2} + b \sqrt{a} + 4 \sqrt{a}$