Solve (-sqrt{14})divsqrt{21}*sqrt{75}

$$( - \sqrt { 14 } ) \div \sqrt { 21 } \times \sqrt { 75 }$$

Evaluate

$$-5\sqrt{2}\approx -7.071067812$$

Solution Steps

Rationalize the denominator of \frac{-\sqrt{14}}{\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$\frac{\left(-\sqrt{14}\right)\sqrt{21}}{\left(\sqrt{21}\right)^{2}}\sqrt{75}$$

The square of \sqrt{21} is 21.

$$\frac{\left(-\sqrt{14}\right)\sqrt{21}}{21}\sqrt{75}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{\left(-\sqrt{14}\right)\sqrt{21}}{21}\times 5\sqrt{3}$$

Express \frac{\left(-\sqrt{14}\right)\sqrt{21}}{21}\times 5 as a single fraction.

$$\frac{\left(-\sqrt{14}\right)\sqrt{21}\times 5}{21}\sqrt{3}$$

Express \frac{\left(-\sqrt{14}\right)\sqrt{21}\times 5}{21}\sqrt{3} as a single fraction.

$$\frac{\left(-\sqrt{14}\right)\sqrt{21}\times 5\sqrt{3}}{21}$$

Factor 21=3\times 7. Rewrite the square root of the product \sqrt{3\times 7} as the product of square roots \sqrt{3}\sqrt{7}.

$$\frac{\left(-\sqrt{14}\right)\sqrt{3}\sqrt{7}\times 5\sqrt{3}}{21}$$

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

$$\frac{\left(-\sqrt{14}\right)\times 3\times 5\sqrt{7}}{21}$$

Multiply 3 and 5 to get 15.

$$\frac{\left(-\sqrt{14}\right)\times 15\sqrt{7}}{21}$$

Divide \left(-\sqrt{14}\right)\times 15\sqrt{7} by 21 to get \left(-\sqrt{14}\right)\times \frac{5}{7}\sqrt{7}.

$$\left(-\sqrt{14}\right)\times \frac{5}{7}\sqrt{7}$$

Multiply -1 and \frac{5}{7} to get -\frac{5}{7}.

$$-\frac{5}{7}\sqrt{14}\sqrt{7}$$

Factor 14=7\times 2. Rewrite the square root of the product \sqrt{7\times 2} as the product of square roots \sqrt{7}\sqrt{2}.

$$-\frac{5}{7}\sqrt{7}\sqrt{2}\sqrt{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$-\frac{5}{7}\times 7\sqrt{2}$$

Cancel out 7 and 7.

$$-5\sqrt{2}$$