Solve sqrt{(15/2-0)^3+(15/2)^2}=

$$\sqrt { ( \frac { 15 } { 2 } - 0 ) ^ { 3 } + ( \frac { 15 } { 2 } ) ^ { 2 } } =$$

Evaluate

$$\frac{15\sqrt{34}}{4}\approx 21.866069606$$

Solution Steps

Subtract 0 from \frac{15}{2} to get \frac{15}{2}.

$$\sqrt{\left(\frac{15}{2}\right)^{3}+\left(\frac{15}{2}\right)^{2}}$$

Calculate \frac{15}{2} to the power of 3 and get \frac{3375}{8}.

$$\sqrt{\frac{3375}{8}+\left(\frac{15}{2}\right)^{2}}$$

Calculate \frac{15}{2} to the power of 2 and get \frac{225}{4}.

$$\sqrt{\frac{3375}{8}+\frac{225}{4}}$$

Add \frac{3375}{8} and \frac{225}{4} to get \frac{3825}{8}.

$$\sqrt{\frac{3825}{8}}$$

Rewrite the square root of the division \sqrt{\frac{3825}{8}} as the division of square roots \frac{\sqrt{3825}}{\sqrt{8}}.

$$\frac{\sqrt{3825}}{\sqrt{8}}$$

Factor 3825=15^{2}\times 17. Rewrite the square root of the product \sqrt{15^{2}\times 17} as the product of square roots \sqrt{15^{2}}\sqrt{17}. Take the square root of 15^{2}.

$$\frac{15\sqrt{17}}{\sqrt{8}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{15\sqrt{17}}{2\sqrt{2}}$$

Rationalize the denominator of \frac{15\sqrt{17}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{15\sqrt{17}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{15\sqrt{17}\sqrt{2}}{2\times 2}$$

To multiply \sqrt{17} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{15\sqrt{34}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{15\sqrt{34}}{4}$$