Solve frac{8sqrt{243}}{sqrt{3}}

$$\frac { 8 \sqrt { 243 } } { \sqrt { 3 } }$$

Evaluate

$$72$$

Solution Steps

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$\frac{8\times 9\sqrt{3}}{\sqrt{3}}$$

Multiply 8 and 9 to get 72.

$$\frac{72\sqrt{3}}{\sqrt{3}}$$

Rationalize the denominator of \frac{72\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{72\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{72\sqrt{3}\sqrt{3}}{3}$$

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

$$\frac{72\times 3}{3}$$

Multiply 72 and 3 to get 216.

$$\frac{216}{3}$$

Divide 216 by 3 to get 72.

$$72$$

Factor

$$2^{3}\times 3^{2}$$