Basic Math Examples

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

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

Step 1

Combine using the product rule for radicals.

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

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

Step 2

Multiply

\frac{3}{16}

$\frac{3}{16}$ by

\frac{3}{9}

$\frac{3}{9}$ .

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

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

Step 3

Reduce the expression

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

$\frac{3 \cdot 3}{16 \cdot 9}$ by cancelling the common factors.

Tap for more steps...

Step 3.1

Factor

3

$3$ out of

3 \cdot 3

$3 \cdot 3$ .

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

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

Step 3.2

Factor

3

$3$ out of

16 \cdot 9

$16 \cdot 9$ .

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

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

Step 3.3

Cancel the common factor.

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

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

Step 3.4

Rewrite the expression.

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

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

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

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

Step 4

Cancel the common factor of

3

$3$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

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

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

Step 4.2

Rewrite the expression.

\sqrt{\frac{1}{16}}

$\sqrt{\frac{1}{16}}$

\sqrt{\frac{1}{16}}

$\sqrt{\frac{1}{16}}$

Step 5

Rewrite

\sqrt{\frac{1}{16}}

$\sqrt{\frac{1}{16}}$ as

\frac{\sqrt{1}}{\sqrt{16}}

$\frac{\sqrt{1}}{\sqrt{16}}$ .

\frac{\sqrt{1}}{\sqrt{16}}

$\frac{\sqrt{1}}{\sqrt{16}}$

Step 6

Any root of

1

$1$ is

1

$1$ .

\frac{1}{\sqrt{16}}

$\frac{1}{\sqrt{16}}$

Step 7

Simplify the denominator.

Tap for more steps...

Step 7.1

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

\frac{1}{\sqrt{4^{2}}}

$\frac{1}{\sqrt{4^{2}}}$

Step 7.2

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

\frac{1}{4}

$\frac{1}{4}$

\frac{1}{4}

$\frac{1}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{1}{4}

$\frac{1}{4}$

Decimal Form:

0.25

$0.25$

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

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

(

)

[

]

√



≥















≤





































