Solve 6sqrt{24}-5sqrt{54}

$$6 \sqrt { 24 } - 5 \sqrt { 54 }$$

Evaluate

$$-3\sqrt{6}\approx -7.348469228$$

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}.

$$6\times 2\sqrt{6}-5\sqrt{54}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{6}-5\sqrt{54}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

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

Multiply -5 and 3 to get -15.

$$12\sqrt{6}-15\sqrt{6}$$

Combine 12\sqrt{6} and -15\sqrt{6} to get -3\sqrt{6}.

$$-3\sqrt{6}$$