Basic Math Examples

$\sqrt{\frac{5}{8}} \cdot \sqrt{\frac{63}{70}}$

Step 1

Combine using the product rule for radicals.

$\sqrt{\frac{5}{8} \cdot \frac{63}{70}}$

Step 2

Multiply $\frac{5}{8}$ by $\frac{63}{70}$ .

$\sqrt{\frac{5 \cdot 63}{8 \cdot 70}}$

Step 3

Reduce the expression $\frac{5 \cdot 63}{8 \cdot 70}$ by cancelling the common factors.

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Step 3.1

Factor $5$ out of $5 \cdot 63$ .

$\sqrt{\frac{5 (63)}{8 \cdot 70}}$

Step 3.2

Factor $5$ out of $8 \cdot 70$ .

$\sqrt{\frac{5 (63)}{5 (8 \cdot 14)}}$

Step 3.3

Cancel the common factor.

$\sqrt{\frac{5 \cdot 63}{5 (8 \cdot 14)}}$

Step 3.4

Rewrite the expression.

$\sqrt{\frac{63}{8 \cdot 14}}$

Step 4

Cancel the common factor of $63$ and $14$ .

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Step 4.1

Factor $7$ out of $63$ .

$\sqrt{\frac{7 (9)}{8 \cdot 14}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $7$ out of $8 \cdot 14$ .

$\sqrt{\frac{7 (9)}{7 (8 \cdot 2)}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{7 \cdot 9}{7 (8 \cdot 2)}}$

Step 4.2.3

Rewrite the expression.

$\sqrt{\frac{9}{8 \cdot 2}}$

Step 5

Multiply $8$ by $2$ .

$\sqrt{\frac{9}{16}}$

Step 6

Rewrite $\sqrt{\frac{9}{16}}$ as $\frac{\sqrt{9}}{\sqrt{16}}$ .

$\frac{\sqrt{9}}{\sqrt{16}}$

Step 7

Simplify the numerator.

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Step 7.1

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

$\frac{\sqrt{3^{2}}}{\sqrt{16}}$

Step 7.2

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

$\frac{3}{\sqrt{16}}$

Step 8

Simplify the denominator.

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Step 8.1

Rewrite $16$ as $4^{2}$ .

$\frac{3}{\sqrt{4^{2}}}$

Step 8.2

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

$\frac{3}{4}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$