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Classify the real numbers as rational or irrational numbers.3/251.16255.15603418923256(141151Rational NumbersIrrational Numbers

Classify the real numbers as rational or irrational numbers.3/251.16255.15603418923256(141151Rational-example-1
User Apelidoko
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The 4th and 6th numbers are the only irrational numbers present

Here, we want to place the numbers into groups

Generally, irrational numbers are numbers that cannot be expressed as a ratio of two integers

Surds are square roots of non-perfect squares

Perfect squares are numbers that have integer roots

Integers are generally whole numbers, positive or negative

Let us take the numbers one after the other;

a) Since root 25 will give an integer square root, then 3 root 25 is a rational number

b) -11/151

This is the ratio of two integers and as such, it is a rational number

c) This is a recursive decimal

the term 1625 keeps recurring

A recurring decimal is a rational number as it can be expressed as the ratio of two numbers using methods of algebra

d) This is not a rational number as it cannot be expressed as the ratio of two integers. We can only have an approximation in this case

e) 256 is a perfect square and as such will give integers as its square root value

f) 141 is not a perfect square and as such, its root is a surd and thus, will not give an integer square root value

User Kevinhyunilkim
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