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Rationalise the following

Rationalise the following-example-1
User Armando
by
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1 Answer

4 votes

Answer:

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)

User TinyGrasshopper
by
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