Basic Math Examples

\frac{\sqrt{35}}{\sqrt{63}}

$\frac{\sqrt{35}}{\sqrt{63}}$

Step 1

Combine

\sqrt{35}

$\sqrt{35}$ and

\sqrt{63}

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

\sqrt{\frac{35}{63}}

$\sqrt{\frac{35}{63}}$

Step 2

Cancel the common factor of

35

$35$ and

63

$63$ .

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Step 2.1

Factor

7

$7$ out of

35

$35$ .

\sqrt{\frac{7 (5)}{63}}

$\sqrt{\frac{7 (5)}{63}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor

7

$7$ out of

63

$63$ .

\sqrt{\frac{7 \cdot 5}{7 \cdot 9}}

$\sqrt{\frac{7 \cdot 5}{7 \cdot 9}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{7 \cdot 5}{7 \cdot 9}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{5}{9}}$

$\sqrt{\frac{5}{9}}$

$\sqrt{\frac{5}{9}}$

Step 3

Rewrite

$\sqrt{\frac{5}{9}}$ as

$\frac{\sqrt{5}}{\sqrt{9}}$ .

$\frac{\sqrt{5}}{\sqrt{9}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite

$9$ as

$3^{2}$ .

$\frac{\sqrt{5}}{\sqrt{3^{2}}}$

Step 4.2

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

$\frac{\sqrt{5}}{3}$

$\frac{\sqrt{5}}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{5}}{3}$

Decimal Form:

$0.74535599 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$