Evaluate 3 square root of 63+2 square root of 7- square root of 28

$3 \sqrt{63} + 2 \sqrt{7} - \sqrt{28}$

Step 1

Simplify each term.

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

Factor $9$ out of $63$ .

$3 \sqrt{9 (7)} + 2 \sqrt{7} - \sqrt{28}$

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

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

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

Pull terms out from under the radical.

$3 (3 \sqrt{7}) + 2 \sqrt{7} - \sqrt{28}$

Multiply $3$ by $3$ .

$9 \sqrt{7} + 2 \sqrt{7} - \sqrt{28}$

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

Factor $4$ out of $28$ .

$9 \sqrt{7} + 2 \sqrt{7} - \sqrt{4 (7)}$

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

$9 \sqrt{7} + 2 \sqrt{7} - \sqrt{2^{2} \cdot 7}$

$9 \sqrt{7} + 2 \sqrt{7} - \sqrt{2^{2} \cdot 7}$

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

$9 \sqrt{7} + 2 \sqrt{7} - 2 \sqrt{7}$

$9 \sqrt{7} + 2 \sqrt{7} - 2 \sqrt{7}$

Step 2

Simplify by adding terms.

Add $9 \sqrt{7}$ and $2 \sqrt{7}$ .

$11 \sqrt{7} - 2 \sqrt{7}$

Subtract $2 \sqrt{7}$ from $11 \sqrt{7}$ .

$9 \sqrt{7}$

$9 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{7}$

Decimal Form:

$23.81176179 \dots$

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