Evaluate 3 square root of 28+ square root of 63

$3 \sqrt{28} + \sqrt{63}$

Step 1

Simplify each term.

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

Factor $4$ out of $28$ .

$3 \sqrt{4 (7)} + \sqrt{63}$

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

$3 \sqrt{2^{2} \cdot 7} + \sqrt{63}$

$3 \sqrt{2^{2} \cdot 7} + \sqrt{63}$

Pull terms out from under the radical.

$3 (2 \sqrt{7}) + \sqrt{63}$

Multiply $2$ by $3$ .

$6 \sqrt{7} + \sqrt{63}$

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

Factor $9$ out of $63$ .

$6 \sqrt{7} + \sqrt{9 (7)}$

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

$6 \sqrt{7} + \sqrt{3^{2} \cdot 7}$

$6 \sqrt{7} + \sqrt{3^{2} \cdot 7}$

Pull terms out from under the radical.

$6 \sqrt{7} + 3 \sqrt{7}$

$6 \sqrt{7} + 3 \sqrt{7}$

Step 2

Add $6 \sqrt{7}$ and $3 \sqrt{7}$ .

$9 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{7}$

Decimal Form:

$23.81176179 \dots$

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