Calculate $4.5$ to the power of $2$ and get $20.25$.
$$\sqrt{\frac{18.5+20.25+5^{2}}{5}-3.3^{2}}$$
Add $18.5$ and $20.25$ to get $38.75$.
$$\sqrt{\frac{38.75+5^{2}}{5}-3.3^{2}}$$
Calculate $5$ to the power of $2$ and get $25$.
$$\sqrt{\frac{38.75+25}{5}-3.3^{2}}$$
Add $38.75$ and $25$ to get $63.75$.
$$\sqrt{\frac{63.75}{5}-3.3^{2}}$$
Expand $\frac{63.75}{5}$ by multiplying both numerator and the denominator by $100$.
$$\sqrt{\frac{6375}{500}-3.3^{2}}$$
Reduce the fraction $\frac{6375}{500}$ to lowest terms by extracting and canceling out $125$.
$$\sqrt{\frac{51}{4}-3.3^{2}}$$
Calculate $3.3$ to the power of $2$ and get $10.89$.
$$\sqrt{\frac{51}{4}-10.89}$$
Convert decimal number $10.89$ to fraction $\frac{1089}{100}$.
$$\sqrt{\frac{51}{4}-\frac{1089}{100}}$$
Least common multiple of $4$ and $100$ is $100$. Convert $\frac{51}{4}$ and $\frac{1089}{100}$ to fractions with denominator $100$.
$$\sqrt{\frac{1275}{100}-\frac{1089}{100}}$$
Since $\frac{1275}{100}$ and $\frac{1089}{100}$ have the same denominator, subtract them by subtracting their numerators.
$$\sqrt{\frac{1275-1089}{100}}$$
Subtract $1089$ from $1275$ to get $186$.
$$\sqrt{\frac{186}{100}}$$
Reduce the fraction $\frac{186}{100}$ to lowest terms by extracting and canceling out $2$.
$$\sqrt{\frac{93}{50}}$$
Rewrite the square root of the division $\sqrt{\frac{93}{50}}$ as the division of square roots $\frac{\sqrt{93}}{\sqrt{50}}$.
$$\frac{\sqrt{93}}{\sqrt{50}}$$
Factor $50=5^{2}\times 2$. Rewrite the square root of the product $\sqrt{5^{2}\times 2}$ as the product of square roots $\sqrt{5^{2}}\sqrt{2}$. Take the square root of $5^{2}$.
$$\frac{\sqrt{93}}{5\sqrt{2}}$$
Rationalize the denominator of $\frac{\sqrt{93}}{5\sqrt{2}}$ by multiplying numerator and denominator by $\sqrt{2}$.
