Precalculus Examples

$\sqrt{s \sqrt{s^{5}}}$

Step 1

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

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Step 1.1

Factor out $s^{4}$ .

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

Step 1.2

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $s$ by $s^{2}$ by adding the exponents.

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Step 3.1

Multiply $s$ by $s^{2}$ .

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Step 3.1.1

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

$\sqrt{s^{1} s^{2} \sqrt{s}}$

Step 3.1.2

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

$\sqrt{s^{1 + 2} \sqrt{s}}$

Step 3.2

Add $1$ and $2$ .

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

Step 4

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

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Step 4.1

Factor out $s^{2}$ .

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

Step 4.2

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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