Solve 6*(1)sqrt{15}*3/5sqrt{20}div(-1/3sqrt{15})

$$6 \cdot ( 1 ) \sqrt { 15 } \times \frac { 3 } { 5 } \sqrt { 20 } \div ( - \frac { 1 } { 3 } \sqrt { 15 } )$$

Evaluate

$$-\frac{108\sqrt{5}}{5}\approx -48.299068314$$

Solution Steps

Cancel out \sqrt{15} in both numerator and denominator.

$$\frac{\frac{3}{5}\times 6\sqrt{20}}{-\frac{1}{3}}$$

Express \frac{3}{5}\times 6 as a single fraction.

$$\frac{\frac{3\times 6}{5}\sqrt{20}}{-\frac{1}{3}}$$

Multiply 3 and 6 to get 18.

$$\frac{\frac{18}{5}\sqrt{20}}{-\frac{1}{3}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{\frac{18}{5}\times 2\sqrt{5}}{-\frac{1}{3}}$$

Express \frac{18}{5}\times 2 as a single fraction.

$$\frac{\frac{18\times 2}{5}\sqrt{5}}{-\frac{1}{3}}$$

Multiply 18 and 2 to get 36.

$$\frac{\frac{36}{5}\sqrt{5}}{-\frac{1}{3}}$$

Divide \frac{36}{5}\sqrt{5} by -\frac{1}{3} by multiplying \frac{36}{5}\sqrt{5} by the reciprocal of -\frac{1}{3}.

$$\frac{\frac{36}{5}\sqrt{5}\times 3}{-1}$$

Anything divided by -1 gives its opposite.

$$-\frac{36}{5}\sqrt{5}\times 3$$

Express -\frac{36}{5}\times 3 as a single fraction.

$$\frac{-36\times 3}{5}\sqrt{5}$$

Multiply -36 and 3 to get -108.

$$\frac{-108}{5}\sqrt{5}$$

Fraction \frac{-108}{5} can be rewritten as -\frac{108}{5} by extracting the negative sign.

$$-\frac{108}{5}\sqrt{5}$$