Evaluate square root of 63+2 square root of 28-5 square root of 7

$\sqrt{63} + 2 \sqrt{28} - 5 \sqrt{7}$

Simplify each term.

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Rewrite $63$ as $3^{2} \cdot 7$ .

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Factor $9$ out of $63$ .

$\sqrt{9 (7)} + 2 \sqrt{28} - 5 \sqrt{7}$

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

$\sqrt{3^{2} \cdot 7} + 2 \sqrt{28} - 5 \sqrt{7}$

Pull terms out from under the radical.

$3 \sqrt{7} + 2 \sqrt{28} - 5 \sqrt{7}$

Rewrite $28$ as $2^{2} \cdot 7$ .

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Factor $4$ out of $28$ .

$3 \sqrt{7} + 2 \sqrt{4 (7)} - 5 \sqrt{7}$

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $2$ .

$3 \sqrt{7} + 4 \sqrt{7} - 5 \sqrt{7}$

Simplify by adding terms.

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Add $3 \sqrt{7}$ and $4 \sqrt{7}$ .

$7 \sqrt{7} - 5 \sqrt{7}$

Subtract $5 \sqrt{7}$ from $7 \sqrt{7}$ .

$2 \sqrt{7}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{7}$

Decimal Form:

$5.29150262 \dots$

Evaluate square root of 63+2 square root of 28-5 square root of 7