Solve 3sqrt{24}-5sqrt{6}-sqrt{12}

$$3 \sqrt { 24 } - 5 \sqrt { 6 } - \sqrt { 12 }$$

Evaluate

$$\sqrt{6}-2\sqrt{3}\approx -1.014611872$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$3\times 2\sqrt{6}-5\sqrt{6}-\sqrt{12}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{6}-5\sqrt{6}-\sqrt{12}$$

Combine 6\sqrt{6} and -5\sqrt{6} to get \sqrt{6}.

$$\sqrt{6}-\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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