Rationalize and simplify the expression 1/(5x(25x^2-2)^(1/2))

 Exercise

$\frac{1}{5x\cdot\sqrt{25x^2-2}}$

 

To rationalize the denominator of the fraction, we multiply the numerator and denominator by $5x\sqrt{25x^2-2}$

$\frac{1}{5x\sqrt{25x^2-2}}\frac{\sqrt{25x^2-2}}{\sqrt{25x^2-2}}$

 

Multiplying fractions $\frac{1}{5x\sqrt{25x^2-2}} \times \frac{\sqrt{25x^2-2}}{\sqrt{25x^2-2}}$

$\frac{\sqrt{25x^2-2}}{5x\sqrt{25x^2-2}\cdot \sqrt{25x^2-2}}$

 

When multiplying two powers that have the same base ($\sqrt{25x^2-2}$), you can add the exponents

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

 

Cancel exponents $\frac{1}{2}$ and $2$

$\frac{\sqrt{25x^2-2}}{5x25x^2-2}$

$\frac{\sqrt{25x^2-2}}{5x25x^2-2}$

 Try other ways to solve this exercise

Can't find a method? Tell us so we can add it.