Prove that 7sqrt{5} is an irrational number. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let us assume,to the contrary,that $7\sqrt{5}$ is a rational number.Then,there exist coprime integers $a$ and $b$ $(b 
eq 0)$ such that $7\sqrt{5

Vedclass · Accepted Answer

Irrational

Vedclass · Answer

(B) Let us assume,to the contrary,that $7\sqrt{5}$ is a rational number.Then,there exist coprime integers $a$ and $b$ $(b 
eq 0)$ such that $7\sqrt{5} = \frac{a}{b}$.Rearranging the equation,we get $\sqrt{5} = \frac{a}{7b}$.Since $a$ and $b$ are integers,$\frac{a}{7b}$ is a rational number.This implies that $\sqrt{5}$ is a rational number.However,this contradicts the fact that $\sqrt{5}$ is an irrational number.Therefore,our assumption is incorrect,and $7\sqrt{5}$ must be an irrational number.

Prove that $7\sqrt{5}$ is an irrational number.

Similar Questions

If $p$ and $q$ are distinct prime integers,then their $LCM$ will be ...........

$\sqrt{2}$ is a . . . . . . number. (Rational,Irrational,Prime)

The value of $\sqrt{1+1}$ is . . . . . . (Rational,Irrational,Integer).

Find the $HCF$ and $LCM$ of $6$ and $20$ using the prime factorization method.

The $LCM$ of $7, 11,$ and $17$ is .......

Vedclass Test Series

Exam Paper Generator

Online Exam Module