Solve 3sqrt{27}divsqrt{6}

$$3 \sqrt{ 27 } \div \sqrt{ 6 }$$

Evaluate

$$\frac{9\sqrt{2}}{2}\approx 6.363961031$$

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}.

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

Multiply 3 and 3 to get 9.

$$\frac{9\sqrt{3}}{\sqrt{6}}$$

Rationalize the denominator of \frac{9\sqrt{3}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{9\sqrt{3}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{9\sqrt{3}\sqrt{6}}{6}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{9\sqrt{3}\sqrt{3}\sqrt{2}}{6}$$

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

$$\frac{9\times 3\sqrt{2}}{6}$$

Multiply 9 and 3 to get 27.

$$\frac{27\sqrt{2}}{6}$$

Divide 27\sqrt{2} by 6 to get \frac{9}{2}\sqrt{2}.

$$\frac{9}{2}\sqrt{2}$$