Question

prove that root 13 and root 17 are irrational numbers

Answer 1

We can prove this by the method of contradiction
Let us assume that √13 is a rational number
√13=p/q
Squaring both sides
13=p^2/q^2
13p^2=q^2 .........(1)

Q^2 is a multiple of 13
Q is also a multiple of 13
Let q^2=13x where x is an integer

Put in (1)
13p^2==(13x)^2
13p^2=169x^2

P^2 =169x^2/13
P^2=13x^2
P^2 is a multiple of 13
P is also a multiple of 13
So they have common multiple 13
But this contradicts our supposition
Hence our assumption is wrong
So √13 is an irrational number

Similarly you can prove for all irrational numbers


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Answer 2

see the above attachment and mark me brainliest