Simplify square root of 7/8* square root of 7/18

$\sqrt{\frac{7}{8}} \cdot \sqrt{\frac{7}{18}}$

Combine using the product rule for radicals.

$\sqrt{\frac{7}{8} \cdot \frac{7}{18}}$

Multiply $\frac{7}{8}$ by $\frac{7}{18}$ .

$\sqrt{\frac{7 \cdot 7}{8 \cdot 18}}$

Multiply.

Multiply $7$ by $7$ .

$\sqrt{\frac{49}{8 \cdot 18}}$

Multiply $8$ by $18$ .

$\sqrt{\frac{49}{144}}$

Rewrite $\sqrt{\frac{49}{144}}$ as $\frac{\sqrt{49}}{\sqrt{144}}$ .

$\frac{\sqrt{49}}{\sqrt{144}}$

Simplify the numerator.

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

$\frac{\sqrt{7^{2}}}{\sqrt{144}}$

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

$\frac{7}{\sqrt{144}}$

Simplify the denominator.

Rewrite $144$ as $12^{2}$ .

$\frac{7}{\sqrt{12^{2}}}$

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

$\frac{7}{12}$

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{12}$

Decimal Form:

$0.58\overline{3}$