Date of submission date : 05.06.2015
1) Are the following statments true or false ? Give reasons for your answers.
i) Every whole number is a natural number
ii) Every integer is a rational number
iii) Every rational number is an integer
2) Find five rational numbers between 1 and 2
3) Is zero a rational number? Can you write it in the form p/q , where p and q are integers and q ≠
4) Find six rational numbers between 3 and 4
5) Find five rational numbers between 3/5 and 4/5
6) State whether the following statements are true or false. Give reasons for your answers
i) Every natural number is a whole number.
ii) Every integer is a whole number
iii) Every rational number is a whole number
7) Locate √2 on the number line
8) Locate √3 on the number line
9) State whether the following statements are true or false. Justify your answers.
i) Every rational number is a real number
ii) Every point on the number line is of the √m, where m is a natural number
iii) Every real number is an irrational number
10) Are the square roots of all positive integers irrational ? If not, give an example of the square
root of a number that is a rational number.
11) Show how √5 can be repesented in the number line
12) Classroom activity ( Constructing a ‘square root spiral’) : Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segmant OP1 of unit length. Draw a line segment P1P2 perpendicular to OP1 of unit length . Now draw a line segment P 2 P 3 perpendicular to OP2 . Then draw a line segment P3 P4 perpendicular to
OP3. Continuing in this manner, you can get the the line segment Pn-1 Pn by drawing a line segment of unit length perpendicular to OP n-1 . In this manner, you will have created the points P2, P3 ,….Pn,…. .., and joined them to create a beautiful spiral depicting √2,√3,√4,…….