Precalculus Examples

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

Step 1

Factor out $s^{2}$ .

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

Step 2

Pull terms out from under the radical.

$\sqrt{s \cdot s \sqrt{s}}$

Step 3

Combine exponents.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Add $1$ and $1$ .

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

Step 4

Pull terms out from under the radical.

$s \sqrt{\sqrt{s}}$

Step 5

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

$s \sqrt[4]{s}$