Solve frac{sqrt{(5+3)^2-1}}{(sqrt{4})^2}

$$\frac { \sqrt { ( 5 + 3 ) ^ { 2 } - 1 } } { ( \sqrt { 4 } ) ^ { 2 } }$$

Evaluate

$$\frac{3\sqrt{7}}{4}\approx 1.984313483$$

Solution Steps

Add 5 and 3 to get 8.

$$\frac{\sqrt{8^{2}-1}}{\left(\sqrt{4}\right)^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{\sqrt{64-1}}{\left(\sqrt{4}\right)^{2}}$$

Subtract 1 from 64 to get 63.

$$\frac{\sqrt{63}}{\left(\sqrt{4}\right)^{2}}$$

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$\frac{3\sqrt{7}}{\left(\sqrt{4}\right)^{2}}$$

The square of \sqrt{4} is 4.

$$\frac{3\sqrt{7}}{4}$$