**Classifying real numbers :**

Even though we can classify real numbers in many ways, it can be classified into two major categories.

They are

(i) Rational numbers

(ii) Irrational numbers

We already know that the set of rational numbers consists of whole numbers, integers, and fractions.

So, the set of real numbers consists of the set of rational numbers and the set of irrational numbers.

It has been illustrated in the picture given below.

**Example 1 : **

Write the name that apply to the number given below.

**√5**

**Answer : **

5 is in square root. It is a whole number, but it is not a perfect square.

So, √5 is irrational, real.

**Example 2 : **

Write the name that apply to the number given below.

**-16.28**

**Answer : **

–16.28 is a terminating decimal.

So, -16.28 is rational, real.

**Example 3 : **

Write the name that apply to the number given below.

**√81 / 9**

**Answer : **

Let us do the possible simplification in the given number.

**√81 / 9 = 9 / 9 **

**√81 / 9 = 1**

**So, √81 / 9 is whole, positive integer, integer, rational, real. **

**Example 4 : **

Write the name that apply to the number given below.

**-9**

**Answer : **

**-9 is negative integer, integer, rational, real.**

**Example 5 : **

Write the name that apply to the number given below.

**9**

**Answer : **

**9 is whole, positive integer, integer, rational, real.**

**Example 6 : **

Write the name that apply to the number given below.

**2√3**

**Answer : **

**We have 3 in square root. 3 is a whole number, but it is not a perfect square. **

**So, √3 is irrational. **

**We already know the fact, if an irrational number is multiplied by a rational number, the product is irrational. **

**Hence, 2****√3 is irrational, real. **

**Example 7 : **

Write the name that apply to the number given below.

**√25**

**Answer : **

**25 is in square root. 25 is a whole number and also it is a perfect square. **

**So, we have **

**√25 = ****√(5x5) = 5**

**Hence, ****√25 is whole, positive integer, integer, rational, real. **

**Example 8 : **

Write the name that apply to the number given below.

**√250**

**Answer : **

**250 is in square root. We are not sure whether 250 is a perfect square or not. **

**So, let us simplify the given number. **

**√250 = ****√(5x5x5x2)**

**√250 = 5****√(5x2)**

**√250 = 5****√10**

**We have 10 in square root. 10 is a whole number, but it is not a perfect square. **

**So, √10 is irrational. **

**We already know the fact, if an irrational number is multiplied by a rational number, the product is irrational. **

**Hence, ****√250**** is irrational, real. **

After having gone through the stuff given above, we hope that the students would have understood "Classifying real numbers".

Apart from the stuff given above, if you want to know more about "Classifying real numbers", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**