Solve -10/sqrt{17*sqrt{37}}

$$\frac{ -10 }{ \sqrt{ 17 } \times \sqrt{ 37 } }$$

Evaluate

$$-\frac{10\sqrt{629}}{629}\approx -0.398726111$$

Solution Steps

To multiply \sqrt{17} and \sqrt{37}, multiply the numbers under the square root.

$$\frac{-10}{\sqrt{629}}$$

Rationalize the denominator of \frac{-10}{\sqrt{629}} by multiplying numerator and denominator by \sqrt{629}.

$$\frac{-10\sqrt{629}}{\left(\sqrt{629}\right)^{2}}$$

The square of \sqrt{629} is 629.

$$\frac{-10\sqrt{629}}{629}$$