Solve 3/2sqrt{27}-5/4sqrt{48}

$$\frac { 3 } { 2 } \sqrt { 27 } - \frac { 5 } { 4 } \sqrt { 48 }$$

Evaluate

$$-\frac{\sqrt{3}}{2}\approx -0.866025404$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{3}{2}\times 3\sqrt{3}-\frac{5}{4}\sqrt{48}$$

Express \frac{3}{2}\times 3 as a single fraction.

$$\frac{3\times 3}{2}\sqrt{3}-\frac{5}{4}\sqrt{48}$$

Multiply 3 and 3 to get 9.

$$\frac{9}{2}\sqrt{3}-\frac{5}{4}\sqrt{48}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{9}{2}\sqrt{3}-\frac{5}{4}\times 4\sqrt{3}$$

Cancel out 4 and 4.

$$\frac{9}{2}\sqrt{3}-5\sqrt{3}$$

Combine \frac{9}{2}\sqrt{3} and -5\sqrt{3} to get -\frac{1}{2}\sqrt{3}.

$$-\frac{1}{2}\sqrt{3}$$