Solve 1/25-2sqrt{6}

$$\frac{ 1 }{ 25-2 \sqrt{ 6 } }$$

Evaluate

$$\frac{2\sqrt{6}+25}{601}\approx 0.049748718$$

Solution Steps

Rationalize the denominator of \frac{1}{25-2\sqrt{6}} by multiplying numerator and denominator by 25+2\sqrt{6}.

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

Consider \left(25-2\sqrt{6}\right)\left(25+2\sqrt{6}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 25 to the power of 2 and get 625.

$$\frac{25+2\sqrt{6}}{625-\left(-2\sqrt{6}\right)^{2}}$$

Expand \left(-2\sqrt{6}\right)^{2}.

$$\frac{25+2\sqrt{6}}{625-\left(-2\right)^{2}\left(\sqrt{6}\right)^{2}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{25+2\sqrt{6}}{625-4\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{25+2\sqrt{6}}{625-4\times 6}$$

Multiply 4 and 6 to get 24.

$$\frac{25+2\sqrt{6}}{625-24}$$

Subtract 24 from 625 to get 601.

$$\frac{25+2\sqrt{6}}{601}$$