## Tamilnadu State Board Class 9 Maths Solutions Chapter 2 Real Numbers Ex 2.3

Question 1.

Represent the following irrational numbers on the number line.

(i) √3

(ii) \(\sqrt { 4.7 }\)

(iii) \(\sqrt { 6.5 }\)

Solution:

(i) √3

(i) Draw a line and mark a point A on it.

(ii) Mark a point B such that AB = 3 cm.

(iii) Mark a point C on this line such that BC = 1 unit.

(iv) Find the midpoint of AC by drawing perpendicular bisector of AC and let it be O.

(v) With O as center and OC = OA as radius, draw a semicircle.

(vi) Draw a line BD, which is perpendicular to AB at B.

(vii) Now BD = √3, which can be marked in the number line as the value of BE = BD = √3

(ii) \(\sqrt { 4.7 }\)

(i) Draw a line and mark a point A on it.

(ii) Mark a point B such that AB = 4.7 cm.

(iii) Mark a point C on this line such that BC = 1 unit.

(iv) Find the midpoint of AC by drawing perpendicular bisector of AC and let it be O.

(v) With O as center and OC = OA as radius, draw a semicircle.

(vi) Draw a line BD, which is perpendicular to AB at B.

(vii) Now BD = \(\sqrt { 4.7 }\), which can be marked in the number line as the value of BE = BD = \(\sqrt { 4.7 }\)

(iii) \(\sqrt { 6.5 }\)

(i) Draw a line and mark a point A on it.

(ii) Mark a point B such that AB = 6.5 cm.

(iii) Mark a point C on this line such that BC = 1 unit.

(iv) Find the midpoint of AC by drawing perpendicular bisector of AC and let it be O.

(v) With O as center and OC = OA as radius, draw a semicircle.

(vi) Draw a line BD, which is perpendicular to AB at B.

(vii) Now BD = \(\sqrt { 6.5 }\), which can be marked in the number line as the value of BE = BD = \(\sqrt { 6.5 }\).

Question 2.

Find any two irrational numbers between

(i) 0.3010011000111…. and 0.3020020002….

(ii) \(\frac { 6 }{ 7 }\) and \(\frac { 12 }{ 13 }\)

(iii) √2 and √3

Solution:

(i) 0.3010011000111…. and 0.3020020002….

Two irrational numbers 0.301202200222 …., 0.301303300333…..

(ii) \(\frac { 6 }{ 7 }\) and \(\frac { 12 }{ 13 }\)

\(\frac { 6 }{ 7 }\) = 0.857142…

\(\frac { 12 }{ 13 }\) = 0.923076

Two irrational numbers between 0.8616611666111……, 0.8717711777111…..

(iii) √2 and √3

√2 = 1.414……

√3 = 1.732….

∴ Two irrational numbers between 1.5155…., 1.6166…….

Question 3.

Find any two rational numbers between 2.2360679….. and 2.236505500….

Solution:

Any two rational numbers are 2.2362, 2.2363