Question

rectionalize the denomination 1upoun
5-angle 7​

Answer 1

Question:-

$\rm Rationalize\:\:\: the\:\:\:Denominator\to \:\dfrac{1}{5-\sqrt{7} }$

Solution:-

→Take

$\rm\implies \dfrac{1}{5-\sqrt{7} }$

→Now multiply and divide by 5+√7

$\rm\implies \dfrac{1}{5-\sqrt{7} }\times\dfrac{5+\sqrt{7} }{5+\sqrt{7} }$

→Use this Identities

$\rm\implies(a-b)(a+b)=a^{2} -b^{2}$

→Now

$\rm\implies \dfrac{5+\sqrt{7} }{5^{2} -(\sqrt{7})^{2} }$

$\rm\implies\dfrac{5+\sqrt{7} }{18}$

→Answer

$\rm\implies\dfrac{5+\sqrt{7} }{18}$

MORE ABOUT

Rationalizing the denominator" is when we move a root (like a square root or cube root) from the bottom of a fraction to the top.

Note: there is nothing wrong with an irrational denominator, it still works. But it is not "simplest form"