Solve (3/2sqrt{5}-sqrt{27})div1/2sqrt{3}

$$( \frac{ 3 }{ 2 } \sqrt{ 5 } - \sqrt{ 27 } ) \div \frac{ 1 }{ 2 } \sqrt{ 3 }$$

Evaluate

$$3\left(\sqrt{15}-6\right)\approx -6.381049961$$

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}.

$$\frac{\frac{3}{2}\sqrt{5}-3\sqrt{3}}{\frac{1}{2}}\sqrt{3}$$

Divide \frac{3}{2}\sqrt{5}-3\sqrt{3} by \frac{1}{2} by multiplying \frac{3}{2}\sqrt{5}-3\sqrt{3} by the reciprocal of \frac{1}{2}.

$$\left(\frac{3}{2}\sqrt{5}-3\sqrt{3}\right)\times 2\sqrt{3}$$

Use the distributive property to multiply \frac{3}{2}\sqrt{5}-3\sqrt{3} by 2.

$$\left(\frac{3}{2}\sqrt{5}\times 2-6\sqrt{3}\right)\sqrt{3}$$

Cancel out 2 and 2.

$$\left(3\sqrt{5}-6\sqrt{3}\right)\sqrt{3}$$

Use the distributive property to multiply 3\sqrt{5}-6\sqrt{3} by \sqrt{3}.

$$3\sqrt{5}\sqrt{3}-6\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$3\sqrt{15}-6\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$3\sqrt{15}-6\times 3$$

Multiply -6 and 3 to get -18.

$$3\sqrt{15}-18$$

Factor

$$3 {(\sqrt{15} - 6)} = -6.381049961$$