prove that x²=18 is irrational. why

Question

nothing

 

Answer 1

As Steve said, irrational numbers cannot be expressed as the ratio of two integers.  By definition an Irrational Number is a real number that cannot be written as a simple fraction.  Look at the problem as given

 

x²=18

x = +-√(18)

x = +-√((9)(2))

x = +-√((3²)(2))

x = +- 3√2

 

x = +-3(1.414213562.......)

 

The √2 is not a rational number and cannot be expressed as the ratio of two integers.  Thus 3√2 is irrational.

Answer 2

Irrational numbers are numbers that have infinite significant digits after the decimal point.

 

Since 18 is not a perfect square, the value of x will be a number between two rational numbers: 4 and 5.  This is because

 

4² = 16          and         5² = 25