Solve sqrt{(10+5)^2/128}

$$\sqrt { \frac { ( 10 + 5 ) ^ { 2 } } { 128 } }$$

Evaluate

$$\frac{15\sqrt{2}}{16}\approx 1.325825215$$

Solution Steps

Add 10 and 5 to get 15.

$$\sqrt{\frac{15^{2}}{128}}$$

Calculate 15 to the power of 2 and get 225.

$$\sqrt{\frac{225}{128}}$$

Rewrite the square root of the division \sqrt{\frac{225}{128}} as the division of square roots \frac{\sqrt{225}}{\sqrt{128}}.

$$\frac{\sqrt{225}}{\sqrt{128}}$$

Calculate the square root of 225 and get 15.

$$\frac{15}{\sqrt{128}}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$\frac{15}{8\sqrt{2}}$$

Rationalize the denominator of \frac{15}{8\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{15\sqrt{2}}{8\times 2}$$

Multiply 8 and 2 to get 16.

$$\frac{15\sqrt{2}}{16}$$