Solve (sqrt{24}-sqrt{54})*1/56

$$( \sqrt { 24 } - \sqrt { 54 } ) \times \frac { 1 } { 56 }$$

Evaluate

$$-\frac{\sqrt{6}}{56}\approx -0.043740888$$

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}.

$$\left(2\sqrt{6}-\sqrt{54}\right)\times \frac{1}{56}$$

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}.

$$\left(2\sqrt{6}-3\sqrt{6}\right)\times \frac{1}{56}$$

Combine 2\sqrt{6} and -3\sqrt{6} to get -\sqrt{6}.

$$-\sqrt{6}\times \frac{1}{56}$$

Multiply -1 and \frac{1}{56} to get -\frac{1}{56}.

$$-\frac{1}{56}\sqrt{6}$$