Solve -4sqrt{21/5}divsqrt{41/11}=

$$- 4 \sqrt { 2 \frac { 1 } { 5 } } \div \sqrt { 4 \frac { 1 } { 11 } } =$$

Evaluate

$$-\frac{44}{15}\approx -2.933333333$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{-4\sqrt{\frac{10+1}{5}}}{\sqrt{\frac{4\times 11+1}{11}}}$$

Add 10 and 1 to get 11.

$$\frac{-4\sqrt{\frac{11}{5}}}{\sqrt{\frac{4\times 11+1}{11}}}$$

Rewrite the square root of the division \sqrt{\frac{11}{5}} as the division of square roots \frac{\sqrt{11}}{\sqrt{5}}.

$$\frac{-4\times \frac{\sqrt{11}}{\sqrt{5}}}{\sqrt{\frac{4\times 11+1}{11}}}$$

Rationalize the denominator of \frac{\sqrt{11}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{-4\times \frac{\sqrt{11}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}{\sqrt{\frac{4\times 11+1}{11}}}$$

The square of \sqrt{5} is 5.

$$\frac{-4\times \frac{\sqrt{11}\sqrt{5}}{5}}{\sqrt{\frac{4\times 11+1}{11}}}$$

To multiply \sqrt{11} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{-4\times \frac{\sqrt{55}}{5}}{\sqrt{\frac{4\times 11+1}{11}}}$$

Express -4\times \frac{\sqrt{55}}{5} as a single fraction.

$$\frac{\frac{-4\sqrt{55}}{5}}{\sqrt{\frac{4\times 11+1}{11}}}$$

Multiply 4 and 11 to get 44.

$$\frac{\frac{-4\sqrt{55}}{5}}{\sqrt{\frac{44+1}{11}}}$$

Add 44 and 1 to get 45.

$$\frac{\frac{-4\sqrt{55}}{5}}{\sqrt{\frac{45}{11}}}$$

Rewrite the square root of the division \sqrt{\frac{45}{11}} as the division of square roots \frac{\sqrt{45}}{\sqrt{11}}.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{\sqrt{45}}{\sqrt{11}}}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{3\sqrt{5}}{\sqrt{11}}}$$

Rationalize the denominator of \frac{3\sqrt{5}}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{3\sqrt{5}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}}$$

The square of \sqrt{11} is 11.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{3\sqrt{5}\sqrt{11}}{11}}$$

To multiply \sqrt{5} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{3\sqrt{55}}{11}}$$

Divide \frac{-4\sqrt{55}}{5} by \frac{3\sqrt{55}}{11} by multiplying \frac{-4\sqrt{55}}{5} by the reciprocal of \frac{3\sqrt{55}}{11}.

$$\frac{-4\sqrt{55}\times 11}{5\times 3\sqrt{55}}$$

Cancel out \sqrt{55} in both numerator and denominator.

$$\frac{-4\times 11}{3\times 5}$$

Cancel out -1 in both numerator and denominator.

$$\frac{4\times 11}{-3\times 5}$$

Multiply 4 and 11 to get 44.

$$\frac{44}{-3\times 5}$$

Multiply -3 and 5 to get -15.

$$\frac{44}{-15}$$

Fraction \frac{44}{-15} can be rewritten as -\frac{44}{15} by extracting the negative sign.

$$-\frac{44}{15}$$

Factor

$$-\frac{44}{15} = -2\frac{14}{15} = -2.933333333333333$$