Examples of irrational & Rational number :

A.

Which numbers are rational number ?

a. √2+√2 

b. 2√2

c. 2

d. √2×√2 

Answer : c&d

c. 

We know 2 is written as 2/1 which is in the form of rational number .

d. When two same irrational numbers are multiply with each other the resultant number is always a rational number thus 

√2×√2 = 2 which is a rational number.

a. When two irrational numbers  add to each other than resultant will also be an irrational number.

thus √2+√2 = √2+√2 is an irrational number.

b. When an irrational number is multiply with an rational number the resultant will be an irrational number.

2 is a rational number while √2 is an irrational number hence 

2√2= √2×√2×√2 = √8 which is an irrational number.

Question 2 : 

Which of in these two numbers  are rational & irrational  number and why?

(a). 3.14

(b). π 

Answer : 

a.  is a rational number because it is write as 

3.14 = 22/7 which is a rational number .

b. π is an irrational number because it is not write as a rational number 

π = 3.141592-------

.

Questions 3 : 

Which one of irrational value is large ?

a. √(4^2+5^2) 

here 4^2 = 16 (here sign "^" comes for power of any number like 4^2 means 4 raise to the power 2 similarly 6^3 = 216 etc ).

b. √(11+12^2)

c. √(6+6)

d. √(4^8)

Answer : b

b. √(11+12^2) = √(155)

 

a. √(4^2+5^2) = √(41) 

C. √(6+6) = √(12)

d. √(4^8) = 256 which is a rational number

In options a,b,c we see that root of 15 {(√15)}

is greater than another two option .

Solve the Questions:

1. Which is Natural number?

a. 9.76

b. 8/9

c. 5003

d. 2π

2. Find the lowest Natural number ?

3. 5^6/6^5 is an?

a. Natural number

b. Rational number 

c. Irrational number

d. None of these