Evaluate square root of 50/49

$\sqrt{\frac{50}{49}}$

Rewrite $\sqrt{\frac{50}{49}}$ as $\frac{\sqrt{50}}{\sqrt{49}}$ .

$\frac{\sqrt{50}}{\sqrt{49}}$

Simplify the numerator.

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

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Factor $25$ out of $50$ .

$\frac{\sqrt{25 (2)}}{\sqrt{49}}$

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

$\frac{\sqrt{5^{2} \cdot 2}}{\sqrt{49}}$

Pull terms out from under the radical.

$\frac{5 \sqrt{2}}{\sqrt{49}}$

Simplify the denominator.

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Rewrite $49$ as $7^{2}$ .

$\frac{5 \sqrt{2}}{\sqrt{7^{2}}}$

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

$\frac{5 \sqrt{2}}{7}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{2}}{7}$

Decimal Form:

$1.01015254 \dots$

Evaluate square root of 50/49

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