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Answer To prove : 3+2√5 is rational number.
Ans: 3 is rational number.
2 is rational number.
2√5 is irrational number (product of rational and irrational is an irrational number)
3+2√5 is an irrational number (sum of rational and irrational number is irrational)
Or
Let P = 3+2√5 is rational number ( we are assuming )
P= 3+2√5
P-3 =2√5
(P-3)÷2=√5
L.H.S. we assume P is a rational number .
P-3 is also rational number substraction of rational number always rational number .
(P-3)÷2 rational number (P-3) divide by rational number 2 hence (P-3)÷2 is rational number .
L.H.S. is rational While R.H.S. √5 is irrational L.H.S ≠R.H.S.
Our assumption is wrong so we can say 3+2√5 is an irrational number.
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Palak Kanti Maitra
I have a degree in Mechanical Engineering I have conducted over 12000 online sessions on Math. durin
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