Solve sqrt{1-8^2/17^2}

$$\sqrt{ 1- \frac{ { 8 }^{ 2 } }{ { 17 }^{ 2 } } }$$

Evaluate

$$\frac{15}{17}\approx 0.882352941$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$\sqrt{1-\frac{64}{17^{2}}}$$

Calculate 17 to the power of 2 and get 289.

$$\sqrt{1-\frac{64}{289}}$$

Convert 1 to fraction \frac{289}{289}.

$$\sqrt{\frac{289}{289}-\frac{64}{289}}$$

Since \frac{289}{289} and \frac{64}{289} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{289-64}{289}}$$

Subtract 64 from 289 to get 225.

$$\sqrt{\frac{225}{289}}$$

Rewrite the square root of the division \frac{225}{289} as the division of square roots \frac{\sqrt{225}}{\sqrt{289}}. Take the square root of both numerator and denominator.

$$\frac{15}{17}$$

Factor

$$\frac{3 \cdot 5}{17} = 0.8823529411764706$$