Solve sqrt{88}+3^4-3/4=

$$\sqrt { 88 } + 3 ^ { 4 } - \frac { 3 } { 4 } =$$

Evaluate

$$2\sqrt{22}+\frac{321}{4}\approx 89.63083152$$

Solution Steps

Factor 88=2^{2}\times 22. Rewrite the square root of the product \sqrt{2^{2}\times 22} as the product of square roots \sqrt{2^{2}}\sqrt{22}. Take the square root of 2^{2}.

$$2\sqrt{22}+3^{4}-\frac{3}{4}$$

Calculate 3 to the power of 4 and get 81.

$$2\sqrt{22}+81-\frac{3}{4}$$

Convert 81 to fraction \frac{324}{4}.

$$2\sqrt{22}+\frac{324}{4}-\frac{3}{4}$$

Since \frac{324}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$2\sqrt{22}+\frac{324-3}{4}$$

Subtract 3 from 324 to get 321.

$$2\sqrt{22}+\frac{321}{4}$$

Factor

$$\frac{8 \sqrt{22} + 321}{4} = 89.63083151964686$$