Evaluate ( square root of 45)/4+( square root of 20)/6

$\frac{\sqrt{45}}{4} + \frac{\sqrt{20}}{6}$

Simplify each term.

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Simplify the numerator.

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Rewrite $45$ as $3^{2} \cdot 5$ .

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Factor $9$ out of $45$ .

$\frac{\sqrt{9 (5)}}{4} + \frac{\sqrt{20}}{6}$

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

$\frac{\sqrt{3^{2} \cdot 5}}{4} + \frac{\sqrt{20}}{6}$

Pull terms out from under the radical.

$\frac{3 \sqrt{5}}{4} + \frac{\sqrt{20}}{6}$

Simplify the numerator.

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Rewrite $20$ as $2^{2} \cdot 5$ .

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Factor $4$ out of $20$ .

$\frac{3 \sqrt{5}}{4} + \frac{\sqrt{4 (5)}}{6}$

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

$\frac{3 \sqrt{5}}{4} + \frac{\sqrt{2^{2} \cdot 5}}{6}$

Pull terms out from under the radical.

$\frac{3 \sqrt{5}}{4} + \frac{2 \sqrt{5}}{6}$

Cancel the common factor of $2$ and $6$ .

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Factor $2$ out of $2 \sqrt{5}$ .

$\frac{3 \sqrt{5}}{4} + \frac{2 (\sqrt{5})}{6}$

Cancel the common factors.

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Factor $2$ out of $6$ .

$\frac{3 \sqrt{5}}{4} + \frac{2 \sqrt{5}}{2 \cdot 3}$

Cancel the common factor.

$\frac{3 \sqrt{5}}{4} + \frac{2 \sqrt{5}}{2 \cdot 3}$

Rewrite the expression.

$\frac{3 \sqrt{5}}{4} + \frac{\sqrt{5}}{3}$

To write $\frac{3 \sqrt{5}}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 \sqrt{5}}{4} \cdot \frac{3}{3} + \frac{\sqrt{5}}{3}$

To write $\frac{\sqrt{5}}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 \sqrt{5}}{4} \cdot \frac{3}{3} + \frac{\sqrt{5}}{3} \cdot \frac{4}{4}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{3 \sqrt{5}}{4}$ and $\frac{3}{3}$ .

$\frac{3 \sqrt{5} \cdot 3}{4 \cdot 3} + \frac{\sqrt{5}}{3} \cdot \frac{4}{4}$

Multiply $4$ by $3$ .

$\frac{3 \sqrt{5} \cdot 3}{12} + \frac{\sqrt{5}}{3} \cdot \frac{4}{4}$

Multiply $\frac{\sqrt{5}}{3}$ and $\frac{4}{4}$ .

$\frac{3 \sqrt{5} \cdot 3}{12} + \frac{\sqrt{5} \cdot 4}{3 \cdot 4}$

Multiply $3$ by $4$ .

$\frac{3 \sqrt{5} \cdot 3}{12} + \frac{\sqrt{5} \cdot 4}{12}$

Combine the numerators over the common denominator.

$\frac{3 \sqrt{5} \cdot 3 + \sqrt{5} \cdot 4}{12}$

Simplify the numerator.

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Multiply $3$ by $3$ .

$\frac{9 \sqrt{5} + \sqrt{5} \cdot 4}{12}$

Move $4$ to the left of $\sqrt{5}$ .

$\frac{9 \sqrt{5} + 4 \cdot \sqrt{5}}{12}$

Add $9 \sqrt{5}$ and $4 \sqrt{5}$ .

$\frac{13 \sqrt{5}}{12}$

The result can be shown in multiple forms.

Exact Form:

$\frac{13 \sqrt{5}}{12}$

Decimal Form:

$2.42240697 \dots$

Evaluate ( square root of 45)/4+( square root of 20)/6

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