Basic Math Examples

\sqrt{\frac{48}{27}}

$\sqrt{\frac{48}{27}}$

Step 1

Cancel the common factor of

48

$48$ and

27

$27$ .

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Step 1.1

Factor

3

$3$ out of

48

$48$ .

\sqrt{\frac{3 (16)}{27}}

$\sqrt{\frac{3 (16)}{27}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor

3

$3$ out of

27

$27$ .

\sqrt{\frac{3 \cdot 16}{3 \cdot 9}}

$\sqrt{\frac{3 \cdot 16}{3 \cdot 9}}$

Step 1.2.2

Cancel the common factor.

$\sqrt{\frac{3 \cdot 16}{3 \cdot 9}}$

Step 1.2.3

Rewrite the expression.

$\sqrt{\frac{16}{9}}$

Step 2

Rewrite

$\sqrt{\frac{16}{9}}$ as

$\frac{\sqrt{16}}{\sqrt{9}}$ .

$\frac{\sqrt{16}}{\sqrt{9}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite

$16$ as

$4^{2}$ .

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

Step 3.2

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

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

Step 4

Simplify the denominator.

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Step 4.1

Rewrite

$9$ as

$3^{2}$ .

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

Step 4.2

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

$\frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$