Algebra Examples

$\sqrt{\frac{7 p^{5}}{63 p}}$

Step 1

Reduce the expression $\frac{7 p^{5}}{63 p}$ by cancelling the common factors.

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Step 1.1

Factor $7$ out of $7 p^{5}$ .

$\sqrt{\frac{7 (p^{5})}{63 p}}$

Step 1.2

Factor $7$ out of $63 p$ .

$\sqrt{\frac{7 (p^{5})}{7 (9 p)}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{7 p^{5}}{7 (9 p)}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{p^{5}}{9 p}}$

Step 2

Cancel the common factor of $p^{5}$ and $p$ .

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Step 2.1

Factor $p$ out of $p^{5}$ .

$\sqrt{\frac{p \cdot p^{4}}{9 p}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $p$ out of $9 p$ .

$\sqrt{\frac{p \cdot p^{4}}{p \cdot 9}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{p \cdot p^{4}}{p \cdot 9}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{p^{4}}{9}}$

Step 3

Simplify the expression.

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Step 3.1

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

$\sqrt{\frac{{(p^{2})}^{2}}{9}}$

Step 3.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{\frac{{(p^{2})}^{2}}{3^{2}}}$

Step 4

Rewrite $\frac{{(p^{2})}^{2}}{3^{2}}$ as ${(\frac{p^{2}}{3})}^{2}$ .

$\sqrt{{(\frac{p^{2}}{3})}^{2}}$

Step 5

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

$\frac{p^{2}}{3}$