Evaluate (16+28 square root of 50)/20

$\frac{16 + 28 \sqrt{50}}{20}$

Step 1

Cancel the common factor of $16 + 28 \sqrt{50}$ and $20$ .

Factor $4$ out of $16$ .

$\frac{4 (4) + 28 \sqrt{50}}{20}$

Factor $4$ out of $28 \sqrt{50}$ .

$\frac{4 (4) + 4 (7 \sqrt{50})}{20}$

Factor $4$ out of $4 (4) + 4 (7 \sqrt{50})$ .

$\frac{4 (4 + 7 \sqrt{50})}{20}$

Cancel the common factors.

Factor $4$ out of $20$ .

$\frac{4 (4 + 7 \sqrt{50})}{4 \cdot 5}$

Cancel the common factor.

$\frac{4 (4 + 7 \sqrt{50})}{4 \cdot 5}$

Rewrite the expression.

$\frac{4 + 7 \sqrt{50}}{5}$

$\frac{4 + 7 \sqrt{50}}{5}$

$\frac{4 + 7 \sqrt{50}}{5}$

Step 2

Simplify the numerator.

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\frac{4 + 7 \sqrt{25 (2)}}{5}$

Rewrite $25$ as $5^{2}$ .

$\frac{4 + 7 \sqrt{5^{2} \cdot 2}}{5}$

$\frac{4 + 7 \sqrt{5^{2} \cdot 2}}{5}$

Pull terms out from under the radical.

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

Multiply $5$ by $7$ .

$\frac{4 + 35 \sqrt{2}}{5}$

$\frac{4 + 35 \sqrt{2}}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{4 + 35 \sqrt{2}}{5}$

Decimal Form:

$10.69949493 \dots$

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