Solve sqrt{24div3}-2sqrt{3*6}

$$\sqrt{ 24 \div 3 } -2 \sqrt{ 3 \times 6 }$$

Evaluate

$$-4\sqrt{2}\approx -5.656854249$$

Solution Steps

Divide 24 by 3 to get 8.

$$\sqrt{8}-2\sqrt{3\times 6}$$

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}.

$$2\sqrt{2}-2\sqrt{3\times 6}$$

Multiply 3 and 6 to get 18.

$$2\sqrt{2}-2\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$2\sqrt{2}-2\times 3\sqrt{2}$$

Multiply 2 and 3 to get 6.

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

Combine 2\sqrt{2} and -6\sqrt{2} to get -4\sqrt{2}.

$$-4\sqrt{2}$$