Question

Q12 Prove that V3 is an irrational number.then prove that 5x V3 is an irrational​

Answer 1

Answer:

Given that, √3 is irrational.

We need to prove, 5 × √3 as Irrational.

Let us assume that 5 × √3 is Rational Number.

Hence, 5 × √3 = p/q - where p and q are co primes.

Now, √3 = p/3q

We observe that Left hand side is irrational where is the right hand sign is rational number.

Hence, our assumption is contradicted.

5 × √3 is Irrational Number

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Rational Number:-

A number which can be represented in the form of p/q where p and q are integers and q is not equal to zero.

Irrational Number:-

A number which can not be represented in the form of p/q where p and q are integers and q is not equal to zero.

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