Question

find area of. quadrant. of circumference 44 cm



prove that root 5 is irrational

Answer 1

1)circumference=44
=>2 πr=44
=>r=44×7/2×22
=>r=7
2) let us assume that root 5 is a rational
LED root 5 = P/q. [ where p and q are integers and q not equal to zero, and p and q are coprime]
( √5) square= p square/ q square
=> p square= 5 q square
therefor, p square is divisible by 5
p is also divisible by 5
again ,let p=5r for some integer r
5rwhole square = 5q square
2 square equal to 5 square
therefore q square is divisible by 5
qis also divisible by 5
therefore p and q have at least 5 as a common factor
this contradicts the fact that p and q are co primes
so our assumption is wrong
therefore root 5 is a irrational