Evaluate (3(25)^(1/2))/2

$\frac{3 {(25)}^{\frac{1}{2}}}{2}$

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Multiply $3$ by $5$ .

$\frac{15}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{2}$

Decimal Form:

$7.5$

Mixed Number Form:

$7 \frac{1}{2}$