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CBSE Class 10 Answered

Prove That Root 5 Is Irrational
Asked by jilsmendapara123 | 28 Jul, 2023, 02:44: PM
answered-by-expert Expert Answer
To prve root 5 is irrational.
Proof:
Suppose space square root of 5 space is space rational
rightwards double arrow square root of 5 equals straight p over straight q comma space where space straight p comma space straight q space are space coprime space integers space and space straight q not equal to 0
rightwards double arrow square root of 5 straight q equals straight p
rightwards double arrow 5 straight q squared equals straight p squared
rightwards double arrow straight q squared equals straight p squared over 5
rightwards double arrow space 5 space divides space straight p squared
rightwards double arrow space 5 space divides space straight p
rightwards double arrow straight p over 5 equals straight r
rightwards double arrow straight p squared equals 25 straight r squared
rightwards double arrow 5 straight q squared equals 25 straight r squared
rightwards double arrow straight q squared equals 5 straight r squared
rightwards double arrow straight r squared equals straight q squared over 5
rightwards double arrow space 5 space divides space straight q squared
rightwards double arrow space 5 space divides space straight q
So comma space straight p space and space straight q space have space straight a space common space factor space 5.
But space this space is space straight a space contradiction.
Hence comma space square root of 5 space is space irrational
Answered by Renu Varma | 28 Jul, 2023, 08:52: PM
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