Basic Math Examples

$\frac{\sqrt{27}}{\sqrt{147}}$

Step 1

Combine $\sqrt{27}$ and $\sqrt{147}$ into a single radical.

$\sqrt{\frac{27}{147}}$

Step 2

Cancel the common factor of $27$ and $147$ .

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Step 2.1

Factor $3$ out of $27$ .

$\sqrt{\frac{3 (9)}{147}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $147$ .

$\sqrt{\frac{3 \cdot 9}{3 \cdot 49}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{3 \cdot 9}{3 \cdot 49}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{9}{49}}$

Step 3

Rewrite $\sqrt{\frac{9}{49}}$ as $\frac{\sqrt{9}}{\sqrt{49}}$ .

$\frac{\sqrt{9}}{\sqrt{49}}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{3^{2}}}{\sqrt{49}}$

Step 4.2

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

$\frac{3}{\sqrt{49}}$

Step 5

Simplify the denominator.

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Step 5.1

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

$\frac{3}{\sqrt{7^{2}}}$

Step 5.2

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

$\frac{3}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{7}$

Decimal Form:

$0.\overline{428571}$