Simplify ( square root of 7)/( square root of 63)

$\frac{\sqrt{7}}{\sqrt{63}}$

Step 1

Combine

$\sqrt{7}$ and

$\sqrt{63}$ into a single radical.

$\sqrt{\frac{7}{63}}$

Step 2

Cancel the common factor of

$7$ and

$63$ .

Factor

$7$ out of

$7$ .

$\sqrt{\frac{7 (1)}{63}}$

Cancel the common factors.

Factor

$7$ out of

$63$ .

$\sqrt{\frac{7 \cdot 1}{7 \cdot 9}}$

Cancel the common factor.

$\sqrt{\frac{7 \cdot 1}{7 \cdot 9}}$

Rewrite the expression.

$\sqrt{\frac{1}{9}}$

Step 3

Rewrite

$\sqrt{\frac{1}{9}}$ as

$\frac{\sqrt{1}}{\sqrt{9}}$ .

$\frac{\sqrt{1}}{\sqrt{9}}$

Step 4

Any root of

$1$ is

$1$ .

$\frac{1}{\sqrt{9}}$

Step 5

Simplify the denominator.

Rewrite

$9$ as

$3^{2}$ .

$\frac{1}{\sqrt{3^{2}}}$

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

$\frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$

Simplify ( square root of 7)/( square root of 63)

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