Simplify ( square root of 10* square root of 21)/( square root of 15)

$\frac{\sqrt{10} \cdot \sqrt{21}}{\sqrt{15}}$

Combine $\sqrt{10}$ and $\sqrt{15}$ into a single radical.

$\sqrt{\frac{10}{15}} \cdot \sqrt{21}$

Combine using the product rule for radicals.

$\sqrt{\frac{10}{15} \cdot 21}$

Combine $\frac{10}{15}$ and $21$ .

$\sqrt{\frac{10 \cdot 21}{15}}$

Reduce the expression $\frac{10 \cdot 21}{15}$ by cancelling the common factors.

Factor $5$ out of $10 \cdot 21$ .

$\sqrt{\frac{5 (2 \cdot 21)}{15}}$

Factor $5$ out of $15$ .

$\sqrt{\frac{5 (2 \cdot 21)}{5 (3)}}$

Cancel the common factor.

$\sqrt{\frac{5 (2 \cdot 21)}{5 \cdot 3}}$

Rewrite the expression.

$\sqrt{\frac{2 \cdot 21}{3}}$

Cancel the common factor of $21$ and $3$ .

Factor $3$ out of $2 \cdot 21$ .

$\sqrt{\frac{3 (2 \cdot 7)}{3}}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\sqrt{\frac{3 (2 \cdot 7)}{3 (1)}}$

Cancel the common factor.

$\sqrt{\frac{3 (2 \cdot 7)}{3 \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{2 \cdot 7}{1}}$

Divide $2 \cdot 7$ by $1$ .

$\sqrt{2 \cdot 7}$

Multiply $2$ by $7$ .

$\sqrt{14}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{14}$

Decimal Form:

$3.74165738 \dots$