Evaluate 4 square root of 7+8 square root of 63

$4 \sqrt{7} + 8 \sqrt{63}$

Step 1

Simplify each term.

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

Factor $9$ out of $63$ .

$4 \sqrt{7} + 8 \sqrt{9 (7)}$

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

$4 \sqrt{7} + 8 \sqrt{3^{2} \cdot 7}$

$4 \sqrt{7} + 8 \sqrt{3^{2} \cdot 7}$

Pull terms out from under the radical.

$4 \sqrt{7} + 8 (3 \sqrt{7})$

Multiply $3$ by $8$ .

$4 \sqrt{7} + 24 \sqrt{7}$

$4 \sqrt{7} + 24 \sqrt{7}$

Step 2

Add $4 \sqrt{7}$ and $24 \sqrt{7}$ .

$28 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$28 \sqrt{7}$

Decimal Form:

$74.08103670 \dots$

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