Question

Find the rationalizing factor of √2 + √7 - √10

Answer 1

Rationalising factor means, the term by which we convert irrational number to rational number . so, it means I have to choose a term by which we make (√2 + √7 - √10) is a rational number.
Let's try to solve .
(√2 + √7 - √10)(√2 + √7 + √10) = (√2 + √7)² - √10²
= 2 + 7 + 2√14 - 10
= 2√14 - 1
= √56 - 1

again, (√56 - 1)(√56 + 1) = 56 - 1 = 55
e.g., (√2 + √7 - 10)[(√2 + √7 + √10)(√56 - 1)] = 55
So, rationalising factor is (√2 + √7 + √10)(√56 + 1)
You can resolve it ,
(√2 + √7 + √10)(√56 + 1)
= √112 + √392 + √560 + √2 + √7 + √10
= 4√7 + 14√2 + 4√35 + √2 + √7 + √10
= 5√7 + 15√2 + 4√35 + √10 [ ans ]