Question

prove that root 5 is a rational number
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Answer 1

Answer:

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.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let √5 is a rational.

So, we can √5=a/b (H. C. F of a and b is 1)

Now,

√5 = a/b

Taking square on both sides

(√5)square = (a/b) square (2 means square).

5=a2/b2

a2= 5b2

a2 is divisible by 5.

a is divisible by 5.

Now,

Let a =5c

a2=(5c)2

5b2=25c2

b2=5c2

b2 is divisible by 5.

b is divisible by 5.

Hence, a and b are divisible by 5

√5 is an irrational.

Proved