Square Root Of 14

Square Root Of 14

Show that the square root of 14 is irrational. Prove your answer?

The square root of (14) is rational.

So square (14) = a / b where a and b are two relative prime numbers, ie they have no common element other than 1.

a / b = square (14) € Ã â € .. squares on both sides of this equation

a 2 / b 2 = 14.

In this case, a 2 is an equal number.

If a is odd, a 2 is odd, then a is also a number. So b, since it has nothing in common with a, it must be strange.

Fact (1) Since b is weird, b 2 is weird.

Since a is also, c = a / 2 is a number and.

c = second

Because a / b = square (14)

a = b * Square (14) ... Divide by the square (14) and change the sides of the equation.

b = a / square (14) ... then.

b = 2c / sqrt (14) â equ We get both sides of this equation:

b 2 = 4c 2/14 ... Divide the digits and the difference by 2 on the right.

b 2 = 2c 2/7.

Therefore, b 2 is the same, which is contrary to reality (1).

The assumption is incorrect and:

sqrt (14) is irrational, it is irrational!

Rational because only perfect squares in squares (4, 16, 25, etc.) are rational.

Square Root Of 14