Question

Prove that √2-3√5 is an irrational number?​

Answer 1

Answer:

please mark me as brainlist

Step-by-step explanation:

hope it helps you to understand

Stay home stay safe

Answer 2

TO PROVE:( 3 - 2√5) is irrational

For proving this , we can apply the theorem “ √5 is an irrational number”

PROOF: Let (3 - √5 ) be a rational number.

=> 3+√5= p/q ( where, p & q are integers, ‘q’ not = 0 )

=> √5 = (p/q) +3

=> √5 = (p+3q)/q

Here, in RHS , numerator is the difference of 2 integers, which always remains an integer. & denominator is also an integer, not = 0.

=> RHS is a rational number ( as, all the conditions for being a rational number, have been satisfied )

But LHS is an irrational number. ( by theorem, √5 is an irrational number)

=> LHS not = RHS

=> our assumption (that 3-√5 is a rational number) is wrong.

Hence, 3-√5 is an irrational number..