Solve 6/sqrt{2+5}

$$\frac { 6 } { \sqrt { 2 } + 5 }$$

Evaluate

$$\frac{30-6\sqrt{2}}{23}\approx 0.935422549$$

Solution Steps

Rationalize the denominator of \frac{6}{\sqrt{2}+5} by multiplying numerator and denominator by \sqrt{2}-5.

$$\frac{6\left(\sqrt{2}-5\right)}{\left(\sqrt{2}+5\right)\left(\sqrt{2}-5\right)}$$

Consider \left(\sqrt{2}+5\right)\left(\sqrt{2}-5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{6\left(\sqrt{2}-5\right)}{\left(\sqrt{2}\right)^{2}-5^{2}}$$

Square \sqrt{2}. Square 5.

$$\frac{6\left(\sqrt{2}-5\right)}{2-25}$$

Subtract 25 from 2 to get -23.

$$\frac{6\left(\sqrt{2}-5\right)}{-23}$$

Use the distributive property to multiply 6 by \sqrt{2}-5.

$$\frac{6\sqrt{2}-30}{-23}$$