Simplify ( square root of 2/5)( square root of 9/2)( square root of 10/3)

$(\sqrt{\frac{2}{5}}) (\sqrt{\frac{9}{2}}) (\sqrt{\frac{10}{3}})$

Step 1

Combine using the product rule for radicals.

$\sqrt{\frac{2}{5} \cdot \frac{9}{2}} \sqrt{\frac{10}{3}}$

Step 2

Combine using the product rule for radicals.

$\sqrt{\frac{2}{5} \cdot \frac{9}{2} \frac{10}{3}}$

Step 3

Multiply $\frac{2}{5}$ by $\frac{9}{2}$ .

$\sqrt{\frac{2 \cdot 9}{5 \cdot 2} \cdot \frac{10}{3}}$

Step 4

Multiply $\frac{2 \cdot 9}{5 \cdot 2}$ by $\frac{10}{3}$ .

$\sqrt{\frac{2 \cdot 9 \cdot 10}{5 \cdot 2 \cdot 3}}$

Step 5

Reduce the expression $\frac{2 \cdot 9 \cdot 10}{5 \cdot 2 \cdot 3}$ by cancelling the common factors.

Cancel the common factor.

$\sqrt{\frac{2 \cdot 9 \cdot 10}{5 \cdot 2 \cdot 3}}$

Rewrite the expression.

$\sqrt{\frac{9 \cdot 10}{5 \cdot 3}}$

Step 6

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9 \cdot 10$ .

$\sqrt{\frac{3 (3 \cdot 10)}{5 \cdot 3}}$

Cancel the common factors.

Factor $3$ out of $5 \cdot 3$ .

$\sqrt{\frac{3 (3 \cdot 10)}{3 \cdot 5}}$

Cancel the common factor.

$\sqrt{\frac{3 (3 \cdot 10)}{3 \cdot 5}}$

Rewrite the expression.

$\sqrt{\frac{3 \cdot 10}{5}}$

Step 7

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $3 \cdot 10$ .

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

Cancel the common factors.

Factor $5$ out of $5$ .

$\sqrt{\frac{5 (3 \cdot 2)}{5 (1)}}$

Cancel the common factor.

$\sqrt{\frac{5 (3 \cdot 2)}{5 \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{3 \cdot 2}{1}}$

Divide $3 \cdot 2$ by $1$ .

$\sqrt{3 \cdot 2}$

Step 8

Multiply $3$ by $2$ .

$\sqrt{6}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\sqrt{6}$

Decimal Form:

$2.44948974 \dots$

Simplify ( square root of 2/5)( square root of 9/2)( square root of 10/3)

Related Questions

Support LCMGCF.com by disabling your adblocker.