Solve frac{sqrt{36-4^2}}{sqrt{4^2}}

$$\frac { \sqrt { 36 - 4 ^ { 2 } } } { \sqrt { 4 ^ { 2 } } }$$

Evaluate

$$\frac{\sqrt{5}}{2}\approx 1.118033989$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{\sqrt{36-16}}{\sqrt{4^{2}}}$$

Subtract 16 from 36 to get 20.

$$\frac{\sqrt{20}}{\sqrt{4^{2}}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{2\sqrt{5}}{\sqrt{4^{2}}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{2\sqrt{5}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{2\sqrt{5}}{4}$$

Divide 2\sqrt{5} by 4 to get \frac{1}{2}\sqrt{5}.

$$\frac{1}{2}\sqrt{5}$$