Question

prove that 2 root 3/5 is irrational. plzzzzzzz solve this question

Answer 1

it cant be written as a fraction of 2 whole numbers... so it's irrational

Answer 2

is it

\[2\sqrt{3/5}\] ? or the 5 is outside

Answer 3

2 root 3/5

=sqrt 2.4 and 2.4 is rational number ( 12/5)

sqrt 2.4 = 1.549193338....... and continues on perhaps infinately

Answer 4

there's no way you can write a non repeating decimal as a fraction of 2 numbers

Answer 5

anwys assume whatever the number you've written is a rational and come up with a contradiction using that statement

Answer 6

Jack is demonstrating that it is so, but not yet proving that it is so.

The usual way is by contradiction.

If \(2\sqrt{\dfrac{3}{5}}\) is rational, it can be expressed as a ratio of two integers in LOWEST FORM. This last part means numerator and denominator have no common factor.

So, if it's rational, we should be able to write: \(2\sqrt{\dfrac{3}{5}} = \dfrac{p}{q}\), where p and q are the reduced integers with no common factor. After a little algebra, we get:

\(3\cdot q^{2} = 5\cdot 2^{2}\cdot p^2\)

What can you say about this expression?