Question

find the rationalise 7+√3/√5+√2​

Answer 1

   Answer:

   $\frac{7\sqrt5 + \sqrt15 - 7\sqrt2 - \sqrt6}{3}$

   Step-by-step explanation:

   The given number is $\frac{7+\sqrt{3} }{\sqrt5+\sqrt2}$

   Rationalizing basically means removing the irrational term from the

   denominator.

   In our case, it is to remove the roots from the denominator

   We can do that by multiplying and dividing the number by $(\sqrt5-\sqrt2)$

⇒ $\frac{7+\sqrt{3} }{\sqrt5+\sqrt2} * \frac{(\sqrt5-\sqrt2)}{(\sqrt5-\sqrt2)}$

   We know that $(a+b)(a-b) = a^{2} - b^{2}$

⇒ $\frac{7+\sqrt{3}(\sqrt5-\sqrt2)}{(\sqrt{5})^{2} - (\sqrt{2})^{2} }$

⇒ $\frac{7\sqrt{5} - 7\sqrt2 + \sqrt15 - \sqrt6 }{5-2}$

∴ $\frac{7\sqrt5 + \sqrt15 - 7\sqrt2 - \sqrt6}{3}$ is our answer