Question

Prove that 6 - root 5 is not a rational no.

Answer 1

Answer:

Rational numbers:

• Rational numbers are the numbers that are in the form of p/q where p and q are integers and q is not equal to zero.

To Prove:

We need to prove that 6-√5 is irrational.

Solution:

Let us assume that 6-√5 is a rational number.

So, we know that any number can be written in the form of p/q where q is not equal to zero.

6-√5 = p/q________(1)

6 - p/q = √5

(6q - p)/q = √5

Here, LHS is in rhe form of a/b which is rational. But RHS is √5 which is irrational.

This contradicts the fact that 6-√5 is rational.

Hence, our assumption is wrong.

Therefore 6-√5 is irrational.

Hence proved!

Answer 2

Answer:

$\implies$ 6 - √5 is irrational.

$\large\underline\mathrm{Given:-}$

• Rational number are the number are in the the form of p/q where p and q are integers and q is not equal to zero.

$\large\underline\mathrm{To \: find}$

• We need to find that 6 - √5 is irrational.

$\large\underline\mathrm{Solution}$

• Let use assume that 6 - √5 is a rational number.
• so, we know that any number can we written in the form of p/q where q is not equal to zero.

$\implies$ 6 - √5 =p/q. ....(1)

$\implies$ 6 - p/q = √5

$\implies$ (6q - p)/q = √5

Now, LHS is the form of a/b which is rational. But RHS is √5 which is irrational

The contradict fact that 6 - √5 is rational.

Hence, it's assumptions is wrong.

Therefore 6 - √5 is irrational.