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Simplify square root of 224/9

$\sqrt{\frac{224}{9}}$

Step 1

Rewrite

$\sqrt{\frac{224}{9}}$ as

$\frac{\sqrt{224}}{\sqrt{9}}$ .

$\frac{\sqrt{224}}{\sqrt{9}}$

Step 2

Simplify the numerator.

Rewrite

$224$ as

$4^{2} \cdot 14$ .

Factor

$16$ out of

$224$ .

$\frac{\sqrt{16 (14)}}{\sqrt{9}}$

Rewrite

$16$ as

$4^{2}$ .

$\frac{\sqrt{4^{2} \cdot 14}}{\sqrt{9}}$

$\frac{\sqrt{4^{2} \cdot 14}}{\sqrt{9}}$

Pull terms out from under the radical.

$\frac{4 \sqrt{14}}{\sqrt{9}}$

$\frac{4 \sqrt{14}}{\sqrt{9}}$

Step 3

Simplify the denominator.

Rewrite

$9$ as

$3^{2}$ .

$\frac{4 \sqrt{14}}{\sqrt{3^{2}}}$

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

$\frac{4 \sqrt{14}}{3}$

$\frac{4 \sqrt{14}}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt{14}}{3}$

Decimal Form:

$4.98887651 \dots$

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