Solve sqrt{24}-sqrt{18}div(2sqrt{8})*sqrt{54})

$$\sqrt { 24 } - \sqrt { 18 } \div ( 2 \sqrt { 8 } ) \times \sqrt { 54 } )$$

Evaluate

$$-\frac{\sqrt{6}}{4}\approx -0.612372436$$

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}.

$$2\sqrt{6}-\frac{\sqrt{18}}{2\sqrt{8}}\sqrt{54}$$

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}.

$$2\sqrt{6}-\frac{3\sqrt{2}}{2\sqrt{8}}\sqrt{54}$$

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}.

$$2\sqrt{6}-\frac{3\sqrt{2}}{2\times 2\sqrt{2}}\sqrt{54}$$

Multiply 2 and 2 to get 4.

$$2\sqrt{6}-\frac{3\sqrt{2}}{4\sqrt{2}}\sqrt{54}$$

Cancel out \sqrt{2} in both numerator and denominator.

$$2\sqrt{6}-\frac{3}{4}\sqrt{54}$$

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}.

$$2\sqrt{6}-\frac{3}{4}\times 3\sqrt{6}$$

Express \frac{3}{4}\times 3 as a single fraction.

$$2\sqrt{6}-\frac{3\times 3}{4}\sqrt{6}$$

Multiply 3 and 3 to get 9.

$$2\sqrt{6}-\frac{9}{4}\sqrt{6}$$

Combine 2\sqrt{6} and -\frac{9}{4}\sqrt{6} to get -\frac{1}{4}\sqrt{6}.

$$-\frac{1}{4}\sqrt{6}$$