Evaluate 2/3* square root of 2.25+1/6* square root of 8100

$\frac{2}{3} \cdot \sqrt{2.25} + \frac{1}{6} \cdot \sqrt{8100}$

Step 1

Simplify each term.

Rewrite $2.25$ as ${1.5}^{2}$ .

$\frac{2}{3} \cdot \sqrt{{1.5}^{2}} + \frac{1}{6} \cdot \sqrt{8100}$

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

$\frac{2}{3} \cdot 1.5 + \frac{1}{6} \cdot \sqrt{8100}$

Cancel the common factor of $1.5$ .

Factor $1.5$ out of $3$ .

$\frac{2}{1.5 (2)} \cdot 1.5 + \frac{1}{6} \cdot \sqrt{8100}$

Cancel the common factor.

$\frac{2}{1.5 \cdot 2} \cdot 1.5 + \frac{1}{6} \cdot \sqrt{8100}$

Rewrite the expression.

$\frac{2}{2} + \frac{1}{6} \cdot \sqrt{8100}$

Divide $2$ by $2$ .

$1 + \frac{1}{6} \cdot \sqrt{8100}$

Rewrite $8100$ as $90^{2}$ .

$1 + \frac{1}{6} \cdot \sqrt{90^{2}}$

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

$1 + \frac{1}{6} \cdot 90$

Cancel the common factor of $6$ .

Factor $6$ out of $90$ .

$1 + \frac{1}{6} \cdot (6 (15))$

Cancel the common factor.

$1 + \frac{1}{6} \cdot (6 \cdot 15)$

Rewrite the expression.

$1 + 15$

Step 2

Add $1$ and $15$ .

$16$