Question

State TRUE or FALSE

$\frac{(2+\sqrt{2})(3-\sqrt{5})}{(3+\sqrt{5})(2-\sqrt{2})}$ is Rational.

• A. True
• B. False

Answer 1

The correct option is B False

$\frac{(2+\sqrt{2})(3-\sqrt{5})}{(3+\sqrt{5})(2-\sqrt{2})}=\frac{{(2+\sqrt{2})}^2{(3-\sqrt{5})}^2}{(9-5)(4-2)}=\frac{(4+2+4\sqrt{2})(9+5-6\sqrt{5})}{8}$

$=\frac{(6+4\sqrt{2})(14-6\sqrt{5})}{8}=\frac{(3+2\sqrt{2})(7-3\sqrt{5})}{2}=\frac{(21-9\sqrt{5}+14\sqrt{2}-6\sqrt{10})}{2}Theabovegivenexpressionconsistsofanalgebraicequationinnumeratorconsistingofirrationalterms,henceitisanirrationalexpression.$
The given statement is false.