Solve =-3/sqrt{45*sqrt{14}}

$$= \frac { - 3 } { \sqrt { 45 } \times \sqrt { 14 } }$$

Evaluate

$$-\frac{\sqrt{70}}{70}\approx -0.119522861$$

Solution Steps

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}.

$$\frac{-3}{3\sqrt{5}\sqrt{14}}$$

To multiply \sqrt{5} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{-3}{3\sqrt{70}}$$

Rationalize the denominator of \frac{-3}{3\sqrt{70}} by multiplying numerator and denominator by \sqrt{70}.

$$\frac{-3\sqrt{70}}{3\left(\sqrt{70}\right)^{2}}$$

The square of \sqrt{70} is 70.

$$\frac{-3\sqrt{70}}{3\times 70}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-\sqrt{70}}{70}$$