Solve sqrt{24}divsqrt{3}-sqrt{6}2sqrt{3}

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

Evaluate

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

Solution Steps

Rewrite the division of square roots \frac{\sqrt{24}}{\sqrt{3}} as the square root of the division \sqrt{\frac{24}{3}} and perform the division.

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

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}.

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

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}.

$$-4\sqrt{2}$$