Solve sqrt{8}(+sqrt[3]{-27}+(1-sqrt{4}))

$$\sqrt { 8 } ( + \sqrt[ 3 ] { - 27 } + ( 1 - \sqrt { 4 } ) )$$

Evaluate

$$-8\sqrt{2}\approx -11.313708499$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}\left(\sqrt[3]{-27}+1-\sqrt{4}\right)$$

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

$$2\sqrt{2}\left(-3+1-\sqrt{4}\right)$$

Add -3 and 1 to get -2.

$$2\sqrt{2}\left(-2-\sqrt{4}\right)$$

Calculate the square root of 4 and get 2.

$$2\sqrt{2}\left(-2-2\right)$$

Subtract 2 from -2 to get -4.

$$2\sqrt{2}\left(-4\right)$$

Multiply 2 and -4 to get -8.

$$-8\sqrt{2}$$