Basic Math Examples

$\frac{\sqrt{28 z^{5}}}{\sqrt{63 z}}$

Step 1

Combine $\sqrt{28 z^{5}}$ and $\sqrt{63 z}$ into a single radical.

$\sqrt{\frac{28 z^{5}}{63 z}}$

Step 2

Reduce the expression $\frac{28 z^{5}}{63 z}$ by cancelling the common factors.

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Step 2.1

Factor $7$ out of $28 z^{5}$ .

$\sqrt{\frac{7 (4 z^{5})}{63 z}}$

Step 2.2

Factor $7$ out of $63 z$ .

$\sqrt{\frac{7 (4 z^{5})}{7 (9 z)}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{7 (4 z^{5})}{7 (9 z)}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{4 z^{5}}{9 z}}$

Step 3

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

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Step 3.1

Factor $z$ out of $4 z^{5}$ .

$\sqrt{\frac{z (4 z^{4})}{9 z}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $z$ out of $9 z$ .

$\sqrt{\frac{z (4 z^{4})}{z \cdot 9}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{z (4 z^{4})}{z \cdot 9}}$

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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

Step 5

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

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

Step 6

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

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

Step 7

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

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