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√5 is irriational

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√5 is irriational

Posted by Golu Gautam 6 years, 3 months ago

CBSE > Class 10 > Mathematics

5 answers

Anisha Raj 6 years, 3 months ago

Yes it is irrational

Yogita Ingle 6 years, 3 months ago

Let us assume that √5 is a rational number.
we know that the rational numbers are in the form of p/q form where p,q are intezers.
so, √5 = p/q
p = √5q
we know that 'p' is a rational number. so √5 q must be rational since it equals to p
but it doesnt occurs with √5 since its not an intezer
therefore, p =/= √5q
this contradicts the fact that √5 is an irrational number
hence our assumption is wrong and √5 is an irrational number.

Ram Dhan 6 years, 3 months ago

Yes

Ádítî Chàûdhäry 6 years, 3 months ago

Therefore, it can be written in the form of p/q. √5=p/q........ equation 1 On squaring both sides (√5)^2=[p/q]^2 5=p^2/q^2 q^2=p^2/5. ..............2 Clearly, p is divisible by 5 Now put q=5a in equation 2 Therefore, 25a^2=5p^2 Therefore,. q is also divisible by 5 Our assumption was wrong √5 is an irrational no. Hence, proved

Ádítî Chàûdhäry 6 years, 3 months ago

Let √5 be a rational no.

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