Solve 18sqrt{15}*1/6sqrt{3}

$$18 \sqrt{ 15 } \times \frac{ 1 }{ 6 \sqrt{ 3 } }$$

Evaluate

$$3\sqrt{5}\approx 6.708203932$$

Solution Steps

Rationalize the denominator of \frac{1}{6\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$18\sqrt{15}\times \frac{\sqrt{3}}{6\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$18\sqrt{15}\times \frac{\sqrt{3}}{6\times 3}$$

Multiply 6 and 3 to get 18.

$$18\sqrt{15}\times \frac{\sqrt{3}}{18}$$

Cancel out 18 and 18.

$$\sqrt{3}\sqrt{15}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$\sqrt{3}\sqrt{3}\sqrt{5}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\sqrt{5}$$