Question

Please help. Free the denominator of the fractionfrom irrationality:

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given

$\frac{2}{5\sqrt{3} }$

To rationalise the denominator, multiply the numerator/ denominator by $\sqrt{3}$

= $\frac{2\sqrt{3} }{5\sqrt{3}(\sqrt{3}) }$

= $\frac{2\sqrt{3} }{15}$

-----------------------------------------------------------------------

Given

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

Multiply the numerator/ denominator by the conjugate of the denominator.

The conjugate of $\sqrt{5}$ - 2 is $\sqrt{5}$ + 2 , then

= $\frac{(\sqrt{5}+2)(\sqrt{5}+2) }{(\sqrt{5}-2)(\sqrt{5}+2) }$ ← expand numerator/denominator using FOIL

= $\frac{5+4\sqrt{5}+4 }{5-4}$

= $\frac{9+4\sqrt{5} }{1}$

= 9 + 4$\sqrt{5}$