Question

rationalize √2+1 by √2-1


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Answer 1

Hey mate

Here is your answer

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Answer 2

Answer:

the answer is 0.4142.  PLEASE SEE THE EXPLANATION AND PLZ MARK ME IN BRAINLIST

Step-by-step explanation:

The given fraction is an irrational one. To rationalize it, we have to multiply its numerator and denominator by a factor which will give a rational product with a rational denominator. Towards this end, we multiply the numerator and the denominator of the given expression by √(√2 - 1) and write,

√(√ 2 - 1)/√(√ 2 + 1) = √(√ 2 - 1)/√(√ 2 + 1) x √(√ 2 - 1)/√(√ 2 - 1)

= [√(√ 2 - 1) x √(√ 2 - 1)] / [√(√ 2 + 1) √(√ 2 - 1)] = (√ 2 - 1) / √[(√ 2 + 1)(√ 2 - 1)]

=(√ 2 - 1) / √[(√2)² - 1² )] = (√2 - 1)/√(2 - 1) = (√2 - 1)/√1 = (√2 - 1)/1 = √2 - 1 (Considering only the positive root).

= 1.4142 - 1 = 0.4142, to 4 decimal figures.