Precalculus Examples

$\sqrt{s \sqrt{s^{8}}}$

Step 1

Rewrite $s^{8}$ as ${(s^{4})}^{2}$ .

$\sqrt{s \sqrt{{(s^{4})}^{2}}}$

Step 2

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

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

Step 3

Multiply $s$ by $s^{4}$ by adding the exponents.

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Step 3.1

Multiply $s$ by $s^{4}$ .

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Step 3.1.1

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

$\sqrt{s^{1} s^{4}}$

Step 3.1.2

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

$\sqrt{s^{1 + 4}}$

Step 3.2

Add $1$ and $4$ .

$\sqrt{s^{5}}$

Step 4

Rewrite $s^{5}$ as ${(s^{2})}^{2} s$ .

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Step 4.1

Factor out $s^{4}$ .

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

Step 4.2

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

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

Step 5

Pull terms out from under the radical.

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