Q8 of 30 Page 14

Find at least two irrational numbers between 2 and 3.

First we square the two given numbers


22 = 4


32 = 9


Square root of any two numbers between 4 and 9 will give an irrational number since they are not perfect squares.


√5 = 2.236067977…


√7 = 2.645751311…


So √5 and √7 are the two irrational numbers between 2 and 3


More from this chapter

All 30 →
6

Find the value of √7 up to six decimal places by long division method.

 7

Locate √10 on number line.

 9

State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.


(ii) Every rational number is a real number.


(iii) Every real number need not be a rational number


(iv) √n is not irrational if n is a perfect square.


(v) √n is irrational if n is not a perfect square.


(vi) All real numbers are irrational.

 1

Visualise 2.874 on the number line, using successive magnification.