Question

show that 3root7 is irrational

Answer 1

Let us take on contrary that 3 root 7 is rational. then there exist two co prime numbers a and b such that 
3root 7 = a/b
=> root 7 = a / 3b
now LHS is an irrational no. whereas RHS is rational
this contradiction has arised due to our wrong assumption in beginning 
therefore 3 root 7 is an irrational number
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Answer 2

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Let us assume 3√7 is a rational number.

Hence it can be written in the form of

$\dfrac {a}{b}$

Where a and b are co-prime.

Hence,

3√7 = $\dfrac {a}{b}$

√7 = $\dfrac {a}{3b}$

Where √7 is IRRRATIONAL no. And [tex]\dfrac{a}{3b} is a RATIONAL no.

Irrational ≠ Rational

Hence our assumption was wrong.

Then,

3√7 is a irrational no.

PrOvEd