Solve -24/sqrt{243}

$$\frac { - 24 } { \sqrt { 243 } }$$

Evaluate

$$-\frac{8\sqrt{3}}{9}\approx -1.539600718$$

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}.

$$\frac{-24}{9\sqrt{3}}$$

Rationalize the denominator of \frac{-24}{9\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{-24\sqrt{3}}{9\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{-24\sqrt{3}}{9\times 3}$$

Cancel out 3 in both numerator and denominator.

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

Multiply 3 and 3 to get 9.

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