Question

Prove that root 5 -3 root 2 is irrational. It should be root 5 not 5

Answer 1

Answer: hi mate here is ur answer

Step-by-step explanation:

step 1 - let us assume √5 is a rational no.

we know that rational nos can be written as p/q

so ,√5 can be written as p/q(where p,q are co-prime )

⇒ √5 =p/q (eq -1)

step 2- square on both sides (eq-1)

⇒5 = p²/q²

⇒5q²= p²

⇒q²= p²/5 (here 5 divides p² that means it also divides p) (eq-2)

step 3 - for 5 dividing p let there be some no called r

⇒p/5= r (sq. on both sides)

⇒ p²/25 = r²(from eq -2 substitute the value of p ²)

⇒5q²/25 = r²

⇒q²/5 = r²

here 5 divides q ² so it also divides q but this is a contradiction to our statement .

hence √5 is irrational

we know that any irrational no. subtracted from any no. gives the result as irrational. so , √5 -√3-2 is an irrational no.

hence proved

hope it helps !!!