find the least rationalising factor for 7-root7
Answers
Least rationalizing factor of (√7-1) = √7(√7+1)
= (√7)²(√7-1)(√7+1)
= 7((√7)²-(1)²)
= 7(7-1)
= 7*6
= 42
∴ Least rationalizing factor = √7(√7+1)
Answer:
Rationalizing factor of 7 - √7 will be 7 + √7
Step-by-step explanation:
Rationalizing factor:
The process of making the numerator of the irrational term into a rational term is known as rationalization. The term which is used to convert the irrational term into a rational term is known as rationalizing factor. Usually the term is multiplied and divide with the irrational term to convert it into a rational term.
The term which are the sum or subtraction of a rational and irrational term will have its conjugate as its rationalizing factor.
For 7 - √7 , 7 + √7 will be its rationalizing factor.
(7-√7)(7+√7)/(7+√7)
=49 - 7/(7+√7)
=42/(7+√7)
42 is a rational term, so the numerator has become rational. Hence 7 + √7 is a rationalizing factor of 7-√7 because by multiplying 7+√7 with 7-√7 , we get 42/(7+√7) , in which numerator is a rational term.