Solve 3/2-sqrt{55}

$$\frac { 3 } { 2 - \sqrt { 55 } }$$

Evaluate

$$\frac{-\sqrt{55}-2}{17}\approx -0.553894029$$

Solution Steps

Rationalize the denominator of \frac{3}{2-\sqrt{55}} by multiplying numerator and denominator by 2+\sqrt{55}.

$$\frac{3\left(2+\sqrt{55}\right)}{\left(2-\sqrt{55}\right)\left(2+\sqrt{55}\right)}$$

Consider \left(2-\sqrt{55}\right)\left(2+\sqrt{55}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{3\left(2+\sqrt{55}\right)}{2^{2}-\left(\sqrt{55}\right)^{2}}$$

Square 2. Square \sqrt{55}.

$$\frac{3\left(2+\sqrt{55}\right)}{4-55}$$

Subtract 55 from 4 to get -51.

$$\frac{3\left(2+\sqrt{55}\right)}{-51}$$

Divide 3\left(2+\sqrt{55}\right) by -51 to get -\frac{1}{17}\left(2+\sqrt{55}\right).

$$-\frac{1}{17}\left(2+\sqrt{55}\right)$$

Use the distributive property to multiply -\frac{1}{17} by 2+\sqrt{55}.

$$-\frac{1}{17}\times 2-\frac{1}{17}\sqrt{55}$$

Express -\frac{1}{17}\times 2 as a single fraction.

$$\frac{-2}{17}-\frac{1}{17}\sqrt{55}$$

Fraction \frac{-2}{17} can be rewritten as -\frac{2}{17} by extracting the negative sign.

$$-\frac{2}{17}-\frac{1}{17}\sqrt{55}$$