Solve sqrt{48}divsqrt{54}

$$\sqrt { 48 } \div \sqrt { 54 }$$

Evaluate

$$\frac{2\sqrt{2}}{3}\approx 0.942809042$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{4\sqrt{3}}{\sqrt{54}}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$\frac{4\sqrt{3}}{3\sqrt{6}}$$

Rationalize the denominator of \frac{4\sqrt{3}}{3\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{4\sqrt{3}\sqrt{6}}{3\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{4\sqrt{3}\sqrt{6}}{3\times 6}$$

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}.

$$\frac{4\sqrt{3}\sqrt{3}\sqrt{2}}{3\times 6}$$

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

$$\frac{4\times 3\sqrt{2}}{3\times 6}$$

Multiply 3 and 6 to get 18.

$$\frac{4\times 3\sqrt{2}}{18}$$

Multiply 4 and 3 to get 12.

$$\frac{12\sqrt{2}}{18}$$

Divide 12\sqrt{2} by 18 to get \frac{2}{3}\sqrt{2}.

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