Precalculus Examples

$\sqrt{s \sqrt{s^{7}}}$

Step 1

Rewrite $s^{7}$ as ${(s^{3})}^{2} s$ .

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Step 1.1

Factor out $s^{6}$ .

$\sqrt{s \sqrt{s^{6} s}}$

Step 1.2

Rewrite $s^{6}$ as ${(s^{3})}^{2}$ .

$\sqrt{s \sqrt{{(s^{3})}^{2} s}}$

$\sqrt{s \sqrt{{(s^{3})}^{2} s}}$

Step 2

Pull terms out from under the radical.

$\sqrt{s \cdot s^{3} \sqrt{s}}$

Step 3

Multiply $s$ by $s^{3}$ by adding the exponents.

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Step 3.1

Multiply $s$ by $s^{3}$ .

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Step 3.1.1

Raise $s$ to the power of $1$ .

$\sqrt{s^{1} s^{3} \sqrt{s}}$

Step 3.1.2

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

$\sqrt{s^{1 + 3} \sqrt{s}}$

$\sqrt{s^{1 + 3} \sqrt{s}}$

Step 3.2

Add $1$ and $3$ .

$\sqrt{s^{4} \sqrt{s}}$

$\sqrt{s^{4} \sqrt{s}}$

Step 4

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

$\sqrt{{(s^{2})}^{2} \sqrt{s}}$

Step 5

Pull terms out from under the radical.

$s^{2} \sqrt{\sqrt{s}}$

Step 6

Rewrite $\sqrt{\sqrt{s}}$ as $\sqrt[4]{s}$ .

$s^{2} \sqrt[4]{s}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$