Solve -3/2sqrt{12}*(-sqrt{27})*1/5sqrt{18}

$$- \frac { 3 } { 2 } \sqrt { 12 } \times ( - \sqrt { 27 } ) \times \frac { 1 } { 5 } \sqrt { 18 }$$

Evaluate

$$\frac{81\sqrt{2}}{5}\approx 22.91025971$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$-\frac{3}{2}\times 2\sqrt{3}\left(-\sqrt{27}\right)\times \frac{1}{5}\sqrt{18}$$

Cancel out 2 and 2.

$$-3\sqrt{3}\left(-\sqrt{27}\right)\times \frac{1}{5}\sqrt{18}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$-3\sqrt{3}\left(-3\sqrt{3}\right)\times \frac{1}{5}\sqrt{18}$$

Multiply -3 and \frac{1}{5} to get \frac{-3}{5}.

$$\frac{-3}{5}\sqrt{3}\left(-3\sqrt{3}\right)\sqrt{18}$$

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$-\frac{3}{5}\sqrt{3}\left(-3\sqrt{3}\right)\sqrt{18}$$

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}.

$$-\frac{3}{5}\sqrt{3}\left(-3\sqrt{3}\right)\times 3\sqrt{2}$$

Express -\frac{3}{5}\times 3 as a single fraction.

$$\frac{-3\times 3}{5}\sqrt{3}\left(-3\sqrt{3}\right)\sqrt{2}$$

Multiply -3 and 3 to get -9.

$$\frac{-9}{5}\sqrt{3}\left(-3\sqrt{3}\right)\sqrt{2}$$

Fraction \frac{-9}{5} can be rewritten as -\frac{9}{5} by extracting the negative sign.

$$-\frac{9}{5}\sqrt{3}\left(-3\sqrt{3}\right)\sqrt{2}$$

Multiply -\frac{9}{5} and -1 to get \frac{9}{5}.

$$\frac{9}{5}\sqrt{3}\times 3\sqrt{3}\sqrt{2}$$

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

$$\frac{9}{5}\sqrt{6}\times 3\sqrt{3}$$

Express \frac{9}{5}\times 3 as a single fraction.

$$\frac{9\times 3}{5}\sqrt{6}\sqrt{3}$$

Multiply 9 and 3 to get 27.

$$\frac{27}{5}\sqrt{6}\sqrt{3}$$

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}.

$$\frac{27}{5}\sqrt{3}\sqrt{2}\sqrt{3}$$

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

$$\frac{27}{5}\times 3\sqrt{2}$$

Express \frac{27}{5}\times 3 as a single fraction.

$$\frac{27\times 3}{5}\sqrt{2}$$

Multiply 27 and 3 to get 81.

$$\frac{81}{5}\sqrt{2}$$