Simplify 5 square root of 20+3 square root of 45

$5 \sqrt{20} + 3 \sqrt{45}$

Simplify each term.

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

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Factor $4$ out of $20$ .

$5 \sqrt{4 (5)} + 3 \sqrt{45}$

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

$5 \sqrt{2^{2} \cdot 5} + 3 \sqrt{45}$

Pull terms out from under the radical.

$5 (2 \sqrt{5}) + 3 \sqrt{45}$

Multiply $2$ by $5$ .

$10 \sqrt{5} + 3 \sqrt{45}$

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

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Factor $9$ out of $45$ .

$10 \sqrt{5} + 3 \sqrt{9 (5)}$

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

$10 \sqrt{5} + 3 \sqrt{3^{2} \cdot 5}$

Pull terms out from under the radical.

$10 \sqrt{5} + 3 (3 \sqrt{5})$

Multiply $3$ by $3$ .

$10 \sqrt{5} + 9 \sqrt{5}$

Add $10 \sqrt{5}$ and $9 \sqrt{5}$ .

$19 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$19 \sqrt{5}$

Decimal Form:

$42.48529157 \dots$

Simplify 5 square root of 20+3 square root of 45

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