Question

Which number is irrational?
a) 0.12345
b) 0.75
c) 2√2 d) 4√2

Answer 1

To determine which number is irrational from the given options, we need to check if the number can be expressed as a fraction or if its decimal representation repeats. The number d) 4√2 is irrational.

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a simple fraction, and its decimal representation goes on forever without repeating. To determine which number is irrational from the given options, we need to check if the number can be expressed as a fraction or if its decimal representation repeats.

a) 0.12345 is a rational number as it can be expressed as 12345/100000.

b) 0.75 is a rational number as it can be expressed as 3/4.

c) 2√2 is an irrational number as the square root of 2 cannot be expressed as a simple fraction.

d) 4√2 is an irrational number as the square root of 2 cannot be expressed as a simple fraction.

Therefore, the number d)

4√2

is irrational.