Solve -8/sqrt{98}

$$\frac{ -8 }{ \sqrt{ 98 } }$$

Evaluate

$$-\frac{4\sqrt{2}}{7}\approx -0.808122036$$

Solution Steps

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{-8}{7\sqrt{2}}$$

Rationalize the denominator of \frac{-8}{7\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-8\sqrt{2}}{7\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-8\sqrt{2}}{7\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-4\sqrt{2}}{7}$$