Solve sqrt{5}*sqrt{7}*sqrt{3}divsqrt{8}

$$\sqrt { 5 } \times \sqrt { 7 } \times \sqrt { 3 } \div \sqrt { 8 }$$

Evaluate

$$\frac{\sqrt{210}}{4}\approx 3.622844187$$

Solution Steps

To multiply \sqrt{5} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{35}\sqrt{3}}{\sqrt{8}}$$

To multiply \sqrt{35} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{105}}{\sqrt{8}}$$

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}.

$$\frac{\sqrt{105}}{2\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{105}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{105}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{105}\sqrt{2}}{2\times 2}$$

To multiply \sqrt{105} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{210}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{210}}{4}$$