Simplify the Radical Expression (5 square root of 15)/(2 square root of 5)

$\frac{5 \sqrt{15}}{2 \sqrt{5}}$

Step 1

Combine $\sqrt{15}$ and $\sqrt{5}$ into a single radical.

$\frac{5 \sqrt{\frac{15}{5}}}{2}$

Step 2

Cancel the common factor of $15$ and $5$ .

Factor $5$ out of $15$ .

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

Cancel the common factors.

Factor $5$ out of $5$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 \sqrt{\frac{3}{1}}}{2}$

Divide $3$ by $1$ .

$\frac{5 \sqrt{3}}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{3}}{2}$

Decimal Form:

$4.33012701 \dots$