Solve sqrt{18}div8*sqrt{21/2}

$$\sqrt { 18 } \div 8 \times \sqrt { \frac { 21 } { 2 } }$$

Evaluate

$$\frac{3\sqrt{21}}{8}\approx 1.718465886$$

Solution Steps

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}.

$$\frac{3\sqrt{2}}{8}\sqrt{\frac{21}{2}}$$

Rewrite the square root of the division \sqrt{\frac{21}{2}} as the division of square roots \frac{\sqrt{21}}{\sqrt{2}}.

$$\frac{3\sqrt{2}}{8}\times \frac{\sqrt{21}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{21}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{2}}{8}\times \frac{\sqrt{21}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{8}\times \frac{\sqrt{21}\sqrt{2}}{2}$$

To multiply \sqrt{21} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{3\sqrt{2}}{8}\times \frac{\sqrt{42}}{2}$$

Multiply \frac{3\sqrt{2}}{8} times \frac{\sqrt{42}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{2}\sqrt{42}}{8\times 2}$$

Factor 42=2\times 21. Rewrite the square root of the product \sqrt{2\times 21} as the product of square roots \sqrt{2}\sqrt{21}.

$$\frac{3\sqrt{2}\sqrt{2}\sqrt{21}}{8\times 2}$$

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

$$\frac{3\times 2\sqrt{21}}{8\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{21}}{8\times 2}$$

Multiply 8 and 2 to get 16.

$$\frac{6\sqrt{21}}{16}$$

Divide 6\sqrt{21} by 16 to get \frac{3}{8}\sqrt{21}.

$$\frac{3}{8}\sqrt{21}$$