Simplify square root of 3/16* square root of 3/9

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

Step 1

Combine using the product rule for radicals.

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

Step 2

Multiply $\frac{3}{16}$ by $\frac{3}{9}$ .

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

Step 3

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

Factor $3$ out of $3 \cdot 3$ .

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

Factor $3$ out of $16 \cdot 9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

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

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

Step 6

Any root of $1$ is $1$ .

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

Step 7

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

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

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

$\frac{1}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$