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Evaluate 2 square root of 44+(17+3) square root of 4

$2 \sqrt{44} + (17 + 3) \sqrt{4}$

Step 1

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$2 \sqrt{4 (11)} + (17 + 3) \sqrt{4}$

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

$2 \sqrt{2^{2} \cdot 11} + (17 + 3) \sqrt{4}$

$2 \sqrt{2^{2} \cdot 11} + (17 + 3) \sqrt{4}$

Step 2

Pull terms out from under the radical.

$2 (2 \sqrt{11}) + (17 + 3) \sqrt{4}$

Step 3

Multiply $2$ by $2$ .

$4 \sqrt{11} + (17 + 3) \sqrt{4}$

Step 4

Add $17$ and $3$ .

$4 \sqrt{11} + 20 \sqrt{4}$

Step 5

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

$4 \sqrt{11} + 20 \sqrt{2^{2}}$

Step 6

Pull terms out from under the radical, assuming positive real numbers.

$4 \sqrt{11} + 20 \cdot 2$

Step 7

Multiply $20$ by $2$ .

$4 \sqrt{11} + 40$

Step 8

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{11} + 40$

Decimal Form:

$53.26649916 \dots$

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