Evaluate 4 square root of 125+ square root of 45-7 square root of 20

$4 \sqrt{125} + \sqrt{45} - 7 \sqrt{20}$

Simplify each term.

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

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Factor $25$ out of $125$ .

$4 \sqrt{25 (5)} + \sqrt{45} - 7 \sqrt{20}$

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

$4 \sqrt{5^{2} \cdot 5} + \sqrt{45} - 7 \sqrt{20}$

Pull terms out from under the radical.

$4 (5 \sqrt{5}) + \sqrt{45} - 7 \sqrt{20}$

Multiply $5$ by $4$ .

$20 \sqrt{5} + \sqrt{45} - 7 \sqrt{20}$

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

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Factor $9$ out of $45$ .

$20 \sqrt{5} + \sqrt{9 (5)} - 7 \sqrt{20}$

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

$20 \sqrt{5} + \sqrt{3^{2} \cdot 5} - 7 \sqrt{20}$

Pull terms out from under the radical.

$20 \sqrt{5} + 3 \sqrt{5} - 7 \sqrt{20}$

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

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Factor $4$ out of $20$ .

$20 \sqrt{5} + 3 \sqrt{5} - 7 \sqrt{4 (5)}$

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

$20 \sqrt{5} + 3 \sqrt{5} - 7 \sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$20 \sqrt{5} + 3 \sqrt{5} - 7 (2 \sqrt{5})$

Multiply $2$ by $- 7$ .

$20 \sqrt{5} + 3 \sqrt{5} - 14 \sqrt{5}$

Simplify by adding terms.

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Add $20 \sqrt{5}$ and $3 \sqrt{5}$ .

$23 \sqrt{5} - 14 \sqrt{5}$

Subtract $14 \sqrt{5}$ from $23 \sqrt{5}$ .

$9 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{5}$

Decimal Form:

$20.12461179 \dots$