Simplify 1/2 square root of 50

$\frac{1}{2} \sqrt{50}$

Step 1

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

Factor $25$ out of $50$ .

$\frac{1}{2} \cdot \sqrt{25 (2)}$

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

$\frac{1}{2} \cdot \sqrt{5^{2} \cdot 2}$

$\frac{1}{2} \cdot \sqrt{5^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$\frac{1}{2} \cdot (5 \sqrt{2})$

Step 3

Multiply $\frac{1}{2} (5 \sqrt{2})$ .

Combine $5$ and $\frac{1}{2}$ .

$\frac{5}{2} \sqrt{2}$

Combine $\frac{5}{2}$ and $\sqrt{2}$ .

$\frac{5 \sqrt{2}}{2}$

$\frac{5 \sqrt{2}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{2}}{2}$

Decimal Form:

$3.53553390 \dots$

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