Solve (sqrt{9})^2+sqrt[3]{-64}-sqrt{17^2-3^2}

$$( \sqrt { 9 } ) ^ { 2 } + \sqrt[ 3 ] { - 64 } - \sqrt { 17 ^ { 2 } - 3 ^ { 2 } }$$

Evaluate

$$5-2\sqrt{70}\approx -11.733200531$$

Solution Steps

The square of \sqrt{9} is 9.

$$9+\sqrt[3]{-64}-\sqrt{17^{2}-3^{2}}$$

Calculate \sqrt[3]{-64} and get -4.

$$9-4-\sqrt{17^{2}-3^{2}}$$

Subtract 4 from 9 to get 5.

$$5-\sqrt{17^{2}-3^{2}}$$

Calculate 17 to the power of 2 and get 289.

$$5-\sqrt{289-3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$5-\sqrt{289-9}$$

Subtract 9 from 289 to get 280.

$$5-\sqrt{280}$$

Factor 280=2^{2}\times 70. Rewrite the square root of the product \sqrt{2^{2}\times 70} as the product of square roots \sqrt{2^{2}}\sqrt{70}. Take the square root of 2^{2}.

$$5-2\sqrt{70}$$