Calculus Examples

$3 \sqrt{\frac{125}{64}}$

Step 1

Rewrite $\sqrt{\frac{125}{64}}$ as $\frac{\sqrt{125}}{\sqrt{64}}$ .

$3 \frac{\sqrt{125}}{\sqrt{64}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $125$ as $5^{2} \cdot 5$ .

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Step 2.1.1

Factor $25$ out of $125$ .

$3 \frac{\sqrt{25 (5)}}{\sqrt{64}}$

Step 2.1.2

Rewrite $25$ as $5^{2}$ .

$3 \frac{\sqrt{5^{2} \cdot 5}}{\sqrt{64}}$

Step 2.2

Pull terms out from under the radical.

$3 \frac{5 \sqrt{5}}{\sqrt{64}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $64$ as $8^{2}$ .

$3 \frac{5 \sqrt{5}}{\sqrt{8^{2}}}$

Step 3.2

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

$3 \frac{5 \sqrt{5}}{8}$

Step 4

Multiply $3 \frac{5 \sqrt{5}}{8}$ .

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Step 4.1

Combine $3$ and $\frac{5 \sqrt{5}}{8}$ .

$\frac{3 (5 \sqrt{5})}{8}$

Step 4.2

Multiply $5$ by $3$ .

$\frac{15 \sqrt{5}}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{15 \sqrt{5}}{8}$

Decimal Form:

$4.19262745 \dots$