Solve (-5/8)^0+14-sqrt{24}-1-sqrt[3]{-27}

$$( - \frac { 5 } { 8 } ) ^ { 0 } + 14 - \sqrt { 24 } - 1 - \sqrt[ 3 ] { - 27 }$$

Evaluate

$$17-2\sqrt{6}\approx 12.101020514$$

Solution Steps

Calculate -\frac{5}{8} to the power of 0 and get 1.

$$1+14-\sqrt{24}-1-\sqrt[3]{-27}$$

Add 1 and 14 to get 15.

$$15-\sqrt{24}-1-\sqrt[3]{-27}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$15-2\sqrt{6}-1-\sqrt[3]{-27}$$

Subtract 1 from 15 to get 14.

$$14-2\sqrt{6}-\sqrt[3]{-27}$$

Calculate \sqrt[3]{-27} and get -3.

$$14-2\sqrt{6}-\left(-3\right)$$

The opposite of -3 is 3.

$$14-2\sqrt{6}+3$$

Add 14 and 3 to get 17.

$$17-2\sqrt{6}$$