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17.
State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.
(ii) Every point on the number line is of the form $square root of straight m comma$ where m is a natural number.
(iii) Every real number is an irrational number.

(i) True, since collection of real numbers is made up of rational and irrational numbers.
(ii) False, because no negative number can be the square root of any natural number.
(iii) False, for example, 2 is real but not irrational.

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18. 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.

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19. Show how

square root of 5

can be represented on the number line.

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20.

Classroom activity (Constructing the ‘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 segment OP₁ of unit length. Draw a line segment P₁ P₂ perpendicular to OP₁ of unit length (see in given Fig.). Now draw a line segment P₂ P₃ perpendicular to OP₂ . Then draw a line segment P₃ P₄ perpendicular to OP₃ . Continuing in this manner, you can get the line segment P_n-1P_n by drawing a line segment of unit length perpendicular to OP_n-1_. In this manner, you will have created the points P₂ , P₃ ,...., P_n ,... ., and joined them to create a beautiful spiral depicting 2, 3, 4, ...

Constructing square root spiral