Solve sqrt{8}*sqrt{18}divsqrt{48}

$$\sqrt{ 8 } \times \sqrt{ 18 } \div \sqrt{ 48 }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2\sqrt{2}\sqrt{18}}{\sqrt{48}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{2\sqrt{2}\times 3\sqrt{2}}{\sqrt{48}}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{2}\sqrt{2}}{\sqrt{48}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{6\times 2}{\sqrt{48}}$$

Multiply 6 and 2 to get 12.

$$\frac{12}{\sqrt{48}}$$

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}.

$$\frac{12}{4\sqrt{3}}$$

Rationalize the denominator of \frac{12}{4\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{12\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{12\sqrt{3}}{4\times 3}$$

Cancel out 3\times 4 in both numerator and denominator.

$$\sqrt{3}$$