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What is the Rationalising factor of 51/3+5-1/3 find the rationalising factor by prrof
Dear student It can be written as 5^1/3 + 5^-1/3rationalizing factor is ( 5^2/3 + 5 ^-2/3 – 1) as when multiplied, this convert in to the formula of a^3 + b^3
Dear student Here is the explanation of above question.Your question is how to rationalize the above expression.The above answer gives you the shortest way to rationalize the expression.For finding rationalizing factor you can use this method. This is somewhat complex .Take 5^1/3=a & 5^-1/3=bNow find the lcm if the exponents.In this case since the denominator is same therefore the LCM is 3Now a^3=5 & b^3=5^-1Since a and b are rational therefore a^3-b^3 is also rationala^3-b^3=(a-b)(a^2+ab+b^2)Rationalizing factor of a-b=(5^1/3–5^-1/3)=5^2/3+5^–2/3+5^2/3*5^-2/3Now just solve the above expression and get the rationalizing factorHope this will help Good Luck
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