Prove that is irrational.

How \”far\” is the square root of two away from being rational?
How \”far\” is the square root of two away from being rational?

CBSE Class 10 Answered

Prove thatsquare root of 5 is irrational.

Asked by roysubarna2016 | 17 Feb, 2019, 11:26: AM

let space square root of 5 space is space rational.... assumption so comma square root of 5 equals straight p over straight q.... straight p space and space straight q space are space co space prime squaring 5 equals straight p squared over straight q squared straight q squared cross times 5 equals straight p squared............. left parenthesis 1 right parenthesis 5 space divides space straight p squared 5 space divides space straight p straight p equals 5 straight a.......... say sub space in space left parenthesis 1 right parenthesis straight q squared cross times 5 equals open parentheses 5 straight a close parentheses squared straight q squared equals 5 open parentheses straight a close parentheses squared 5 space divides space straight q so space 5 space divides space both space straight p space and space straight q but space that space can apostrophe straight t space be space true space since space straight p space and space straight q space are space co space prime so space assumption space is space wrong square root of 5 space is space irrational

Answered by Arun | 17 Feb, 2019, 12:37: PM

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Answer the following in one word, one sentence or as per the exact requirement : (a) Let p and q be two distinct prime numbers. Write HCF (p , q). (b) Fill in the blank space in the statement given below : (i) If p be a prime, then √p is _______number. (ii) If p/q is a rational number then p and q are _____ . (c) √27 is an irrational number. Justify the statement.question image

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