Algebra Examples

$\sqrt{\sqrt[3]{49 r^{6} s^{4}}}$

Step 1

Rewrite $49 r^{6} s^{4}$ as ${(r^{2} s)}^{3} \cdot (49 s)$ .

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Step 1.1

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

$\sqrt{\sqrt[3]{49 {(r^{2})}^{3} s^{4}}}$

Step 1.2

Factor out $s^{3}$ .

$\sqrt{\sqrt[3]{49 {(r^{2})}^{3} (s^{3} s)}}$

Step 1.3

Move $49$ .

$\sqrt{\sqrt[3]{{(r^{2})}^{3} s^{3} \cdot 49 s}}$

Step 1.4

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

$\sqrt{\sqrt[3]{{(r^{2} s)}^{3} \cdot 49 s}}$

Step 1.5

Add parentheses.

$\sqrt{\sqrt[3]{{(r^{2} s)}^{3} \cdot (49 s)}}$

Step 2

Pull terms out from under the radical.

$\sqrt{r^{2} s \sqrt[3]{49 s}}$

Step 3

Rewrite $r^{2} s \sqrt[3]{49 s}$ as $r^{2} (s \sqrt[3]{7^{2} s})$ .

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Step 3.1

Rewrite $49$ as $7^{2}$ .

$\sqrt{r^{2} s \sqrt[3]{7^{2} s}}$

Step 3.2

Add parentheses.

$\sqrt{r^{2} (s \sqrt[3]{7^{2} s})}$

Step 4

Pull terms out from under the radical.

$r \sqrt{s \sqrt[3]{7^{2} s}}$

Step 5

Raise $7$ to the power of $2$ .

$r \sqrt{s \sqrt[3]{49 s}}$