Solve sqrt{4}(-sqrt{3}+2sqrt{8})

$$\sqrt { 4 } ( - \sqrt { 3 } + 2 \sqrt { 8 } )$$

Evaluate

$$8\sqrt{2}-2\sqrt{3}\approx 7.849606884$$

Solution Steps

Calculate the square root of 4 and get 2.

$$2\left(-\sqrt{3}+2\sqrt{8}\right)$$

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}.

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

Multiply 2 and 2 to get 4.

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

Use the distributive property to multiply 2 by -\sqrt{3}+4\sqrt{2}.

$$2\left(-\sqrt{3}\right)+8\sqrt{2}$$

Multiply 2 and -1 to get -2.

$$-2\sqrt{3}+8\sqrt{2}$$