Solve (10+5)^2/sqrt{44}+24

$$\frac { ( 10 + 5 ) ^ { 2 } } { \sqrt { 44 } } + 24$$

Evaluate

$$\frac{225\sqrt{11}}{22}+24\approx 57.920026265$$

Short Solution Steps

Add 10 and 5 to get 15.

$$\frac{15^{2}}{\sqrt{44}}+24$$

Calculate 15 to the power of 2 and get 225.

$$\frac{225}{\sqrt{44}}+24$$

Factor 44=2^{2}\times 11. Rewrite the square root of the product \sqrt{2^{2}\times 11} as the product of square roots \sqrt{2^{2}}\sqrt{11}. Take the square root of 2^{2}.

$$\frac{225}{2\sqrt{11}}+24$$

Rationalize the denominator of \frac{225}{2\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{225\sqrt{11}}{2\left(\sqrt{11}\right)^{2}}+24$$

The square of \sqrt{11} is 11.

$$\frac{225\sqrt{11}}{2\times 11}+24$$

Multiply 2 and 11 to get 22.

$$\frac{225\sqrt{11}}{22}+24$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 24 times \frac{22}{22}.

$$\frac{225\sqrt{11}}{22}+\frac{24\times 22}{22}$$

Since \frac{225\sqrt{11}}{22} and \frac{24\times 22}{22} have the same denominator, add them by adding their numerators.

$$\frac{225\sqrt{11}+24\times 22}{22}$$

Do the multiplications in 225\sqrt{11}+24\times 22.

$$\frac{225\sqrt{11}+528}{22}$$