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Asked by Arun Last Modified
Answer 
Tasneem
(i) Assume that is Rational.
Hence,
is rational as a and b are integers.
Hence is rational which contradicts the fact that
is irrational.
Therefore, our assumption was incorrect and is irrational.
(ii) Assume that 7 is rational.
where a and b are some integers.
therefore,
a and 7b are ratonal and so is
But this contradicts the fact that is irrational.
Hence our assumption was incorrect and is rational.
(iii) Assume as rational
Since a and b are integers, is also rational and
should be rational as well.
This contradicts the fact that is irrational and hence our assumption was incorrect.
is irrational.
1) 1⁄√2
Rationalise this number 1 *√2⁄√2 *√2
= √2/2
√2 is irrational number and 2 is rational number division of rational number by irrational number is irrational . Hence 1/√2 is an irrational number.
2)7√5
7 is rational number √5 is an irrational number product of rarional and irrational number is irrational number.
3)6+√5
6 is a rational number √5 is irrational number sum of rational and irrational number 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
(i)Let is a rational number=. Squaring both sides ½=, So b^2=2a^2.So b^2 is divisible by 2 and b is divisible by 2. Let b=2c where c is an integer. Then b^2=4c^2, Hence 2a^2=4c^2. and a^2=2c^2.so a^2 is divisible by 2 and a is divisible by 2.This shows a and b have a common factor 2. But for a rational number a/b there cannot be a common factor other than 1.So this contradicts 1/√2 is rational. So it is an irrational number.
(ii) Let 7√5 is a rational number=a/b.
then√5=a/7b is a rational number. But we know√5 is irrational. So 7√5 is irrational.
(iii)Let 6+√2 is a rational number=a/b
then√2=(a/b)-6=(a-6b)/6 is a rational number.
This contradicts √2 is irrational.
So 6+√2 is irrational.
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