Question

Rationalise the following

Answer 1

a)
`-((2√(3)+5√(2))^2)/(38)`

b)
`(5√(7)+2 )/(171)`

Explanation:

`a) (2√(3)+5√(2) )/(2√(3)-5√(2) )`

Remember this property;

`(1)/(√(x)+√(y) )*(√(x)-√(y))/(√(x)-√(y))=(√(x)-√(y))/((√(x))^2-(√(y))^2 ) =(√(x)-√(y) )/(x-y)`

We multiply by the same denominator with opposite sign, that gives us a result of the same denominator with each term squared which will cause the term to come out of the root.

Now let's do it with your own equation.

`(2√(3)+5√(2) )/(2√(3)-5√(2) )*(2√(3)+5√(2))/(2√(3)+5√(2)) =((2√(3)+5√(2))^2)/((2√(3))^2-(5√(2))^2)= ((2√(3)+5√(2))^2)/((4*3)-(25*2))=((2√(3)+5√(2))^2)/(12-50)=((2√(3)+5√(2))^2)/(-38)`

Now let's try with b.

`b)(1)/(5√(7)-2 ) *(5√(7)+2)/(5√(7)+2)=(5√(7)+2 )/((5√(7))^2-(2)^2 )=(5√(7)+2 )/(25*7-4)=(5√(7)+2 )/(175-4)=(5√(7)+2 )/(171)`