Solve sqrt{30}*sqrt{22/3}*sqrt{0.4}

$$\sqrt { 30 } \times \sqrt { 2 \frac { 2 } { 3 } } \times \sqrt { 0.4 }$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\sqrt{30}\sqrt{\frac{6+2}{3}}\sqrt{0.4}$$

Add 6 and 2 to get 8.

$$\sqrt{30}\sqrt{\frac{8}{3}}\sqrt{0.4}$$

Rewrite the square root of the division \sqrt{\frac{8}{3}} as the division of square roots \frac{\sqrt{8}}{\sqrt{3}}.

$$\sqrt{30}\times \frac{\sqrt{8}}{\sqrt{3}}\sqrt{0.4}$$

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}.

$$\sqrt{30}\times \frac{2\sqrt{2}}{\sqrt{3}}\sqrt{0.4}$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\sqrt{30}\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{0.4}$$

The square of \sqrt{3} is 3.

$$\sqrt{30}\times \frac{2\sqrt{2}\sqrt{3}}{3}\sqrt{0.4}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\sqrt{30}\times \frac{2\sqrt{6}}{3}\sqrt{0.4}$$

Express \sqrt{30}\times \frac{2\sqrt{6}}{3} as a single fraction.

$$\frac{\sqrt{30}\times 2\sqrt{6}}{3}\sqrt{0.4}$$

Factor 30=6\times 5. Rewrite the square root of the product \sqrt{6\times 5} as the product of square roots \sqrt{6}\sqrt{5}.

$$\frac{\sqrt{6}\sqrt{5}\times 2\sqrt{6}}{3}\sqrt{0.4}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{6\times 2\sqrt{5}}{3}\sqrt{0.4}$$

Multiply 6 and 2 to get 12.

$$\frac{12\sqrt{5}}{3}\sqrt{0.4}$$

Divide 12\sqrt{5} by 3 to get 4\sqrt{5}.

$$4\sqrt{5}\sqrt{0.4}$$

To multiply \sqrt{5} and \sqrt{0.4}, multiply the numbers under the square root.

$$4\sqrt{2}$$