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

Square Root Of 14

Show that the square root of 14 is irrational. Explain your answer? 3

Make the square root of (14) rational.

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

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

a 2 / b 2 = 14

In this case, a 2 is an even number.

If a is odd, a 2 is odd, then a is also an even number. So b, since it has no common factor with a, it must be odd.

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

Since a is equal to, c = a / 2 is a number and

c = 2nd

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) مر Squaring both sides of this equation gives us:

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

b 2 = 2c 2/7

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

The hypothesis is incorrect and:

sqrt (14) is irrational, it is irrational!

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

Square Root Of 14