Question

show that 3root 5 -1 is not a rational number , means 3root 5-1 is irrational

please answer fasttt
and in stepss
give the correct answer

Answer 1

let 3root5 be a/b
3root5=a/b
by squaring both side
45b^2=a^2...........eq1
now,let 3root5=b/c
by sqaring both side
45c^2=b^2............eq2
so ,in eq1 and eq2 Factors are same
and in rational nos. factors are not same



............ty

Answer 2

Howdy !!

your answer is here ---

Let us suppose that 3√5-1 is a rational

so, 3√5-1 = a/b where a and b are integers and b is not equal to 0


=> 3√5 = a+b/b

=> √5 = a+b/3b

now, a+b/5b is a rational number [ since a and b are integer ]

so, √5 is also a rational no. [√5 = a+b/3b]

but this contradict the fact that √5 is irrational .

therefore, our assumption is wrong

hence , 3√5-1 is irrational ..


hope it help you
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