Show whether √15 is rational or irrational.
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Answered by
42
√15 is rational ( contradiction method).
√15=a/b
(a and b are not common factor).
squaring on both sides, we get,
15= a^2/b^2.
15b^2=a^2 (a=15c)
b^2=15/a^2
(assume, a^2 =225c^2)
15b^2=225c^2
b^2=225c^2/15
b^2=15c^2
c^2=15/b^2
c =15/b.
15 divided both a and b which is a contradiction.
ie, √15 is irrational.
√15=a/b
(a and b are not common factor).
squaring on both sides, we get,
15= a^2/b^2.
15b^2=a^2 (a=15c)
b^2=15/a^2
(assume, a^2 =225c^2)
15b^2=225c^2
b^2=225c^2/15
b^2=15c^2
c^2=15/b^2
c =15/b.
15 divided both a and b which is a contradiction.
ie, √15 is irrational.
Answered by
35
it is an irrational number.because if we expand it it will come as root 3 and 5.root 3 and root 5 are irrational numbers.there is no perfect square value to them.the product of two irrational numbers is a rational number.
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