Math, asked by afnanfayha786, 11 months ago

prove that 5 root 2 + 3 is irrational​

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Answered by shafaq24
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Answered by sonabrainly
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Step-by-step explanation:

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Let us assume that 5+2 root 3 is rational

5+2 root 3 = p/q ( where p and q are co prime)

2root 3 = p/q-5

2 root 3 = p-5q/q

root  3 = p-5q/2q

now p , 5 , 2 and q are integers 

 p-5q/2q is rational

 root 3 is rational

but we know that root 3 is irrational . This is a contradiction which has arisen due to our wrong assumption.

5+2 root 3 is irrational

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