Solve frac{sqrt{18}-sqrt{98}}{sqrt{128}}

$$\frac { \sqrt { 18 } - \sqrt { 98 } } { \sqrt { 128 } }$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{3\sqrt{2}-\sqrt{98}}{\sqrt{128}}$$

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}.

$$\frac{3\sqrt{2}-7\sqrt{2}}{\sqrt{128}}$$

Combine 3\sqrt{2} and -7\sqrt{2} to get -4\sqrt{2}.

$$\frac{-4\sqrt{2}}{\sqrt{128}}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$\frac{-4\sqrt{2}}{8\sqrt{2}}$$

Cancel out 4\sqrt{2} in both numerator and denominator.

$$\frac{-1}{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$-\frac{1}{2}$$

Factor

$$-\frac{1}{2} = -0.5$$