Question

Prove that √(5/25 ) is irrational.

Answer 1

√(5/25) = √(1/5) = 1/√5 = √5/5

Mathematical generality :- Any number obtained on dividing a irrational with natural number is also irrational

We will prove whether √5/5 is irrational by contradiction method. 
Let √5/5 be rational 
It can be expressed as √5/5 = a/b ( where a, b are integers and co-primes. 
√5/5 = a/b
5= 25a²/b² 
5b² = 25a²
b² =5a²
5 divides b²
By the Fundamental theorem of Arithmetic 
so, 5 divides b.

b = 5k (for some integer) 

5a² = 25k² 
a² = 5k² 
a² = 5k² 

5 divides a²
5 divides a. 

Now 5 divides both a & b this contradicts the fact that they are co primes. 
this happened due to faulty assumption that √5/5 is rational. Hence, √5/5 is irrational. 

Hence, Proved that √(5/25) is irrational.

We could also have proved it by irrational proof of √5 and using mathematical generality as mentioned earlier in the solution

Read more on Brainly.in - brainly.in/question/2646257#readmore

Answer 2

hay!

we will be prove whether _/5/5 is irrational by contradictio method

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_/5/5 =a/b

primers :
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_/5/5=a/b

5=25a²/b²

5b²=25a²

b²=5a²

5 Dividesb

b=5p

5a²=25p²

a²=5p²

5 divides a²

so its co primers

HENCE PROVED

_/5/25 IS irrational
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I hope it's help you