AP State Syllabus AP Board 9th Class Maths Solutions Chapter 1 Real Numbers Ex 1.2 Textbook Questions and Answers.

## AP State Syllabus 9th Class Maths Solutions 1st Lesson Real Numbers Exercise 1.2

Question 1.

Classify the following numbers as rational or irrational.

i) \(\sqrt{27}\)

ii) \(\sqrt{441}\)

iii) 30.232342345

iv) 7.484848

v) 11.2132435465

vi) 0.3030030003

Solution:

i) \(\sqrt{27}\) – irrational number

ii) \(\sqrt{441}\) = 21 – rational

iii) 30.232342345 – irrational number

iv) 7.484848 – rational number

v) 11.2132435465 – irrational number

vi) 0.3030030003 – irrational number

Question 2.

Explain with an example how irrational numbers differ from rational numbers ?

Solution:

Irrational numbers can’t be expressed in \(\frac { p }{ q }\) form where p and q are integers and q ≠ 0.

E.g.\(\sqrt{2}, \sqrt{3} ; \sqrt{5}, \sqrt{7}\) etc.

Where as a rational can be expressed in \(\frac { p }{ q }\) form

E.g. :- -3 = \(\frac { -3 }{ 1 }\) and \(\frac { 5 }{ 4 }\) etc.

Question 3.

Find an irrational number between \(\frac { 5 }{ 7 }\) and \(\frac { 7 }{ 9 }\). How many more there may be ?

Solution :

The decimal forms of \(\frac { 5 }{ 7 }\) and \(\frac { 7 }{ 9 }\) are

\(\frac{5}{7}=0 . \overline{714285} \ldots ., \frac{7}{9}=0.7777 \ldots \ldots=0 . \overline{7}\)

∴ An irrational between \(\frac { 5 }{ 7 }\) and \(\frac { 7 }{ 9 }\) is 0.727543…………

There are infinitely many irrational numbers between \(\frac { 5 }{ 7 }\) and \(\frac { 7 }{ 9 }\).

Question 4.

Find two irrational numbers between 0.7 and 0.77.

Solution:

Two irrational numbers between 0.7 and 0.77 can take the form

0.70101100111000111…………. and 0.70200200022……………

Question 5.

Find the value of √5 uPto 3 decimal places.

Solution:

[√5 is not exactly equal to 2.2350679………….. as shown ¡n calculators]

Question 6.

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

Solution:

Question 7.

Locate \(\sqrt{\mathrm{10}}\) on number line.

Step – 1 : Draw a number line.

Step – 2 : Draw a rectangle OABC at zero with measures 3 x 1. i.e., length 3 units and breadth 1 unit.

Step – 3 : Draw the diagonal OB.

Step – 4 : Draw an arc with centre ‘O’ and radius OB which cuts the number line at D.

Step – 5 : ‘D’ represents \(\sqrt{\mathrm{10}}[latex] on the number line.

Question 8.

Find atleast two irrational numbers between 2 and 3.

Solution:

An irrational number between a and b is Tab [latex]\sqrt{\mathrm{ab}}\) unless ab is a perfect square.

∴ Irrational number between 2 and 3 is √6

∴ Required irrational numbers are 6^{1/2}, 24^{1/4}

Method – II:

Irrational numbers between 2 and 3 are of the form 2.12111231234………….. and 3.13113111311113…….

Question 9.

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

Solution:

- Every irrational number is a real number – True (since real numbers consist of rational numbers and irrational numbers)
- Every rational number is a real number – True (same as above)
- Every rational number need not be a rational number – False (since all rational numbers are real numbers).
- \(\sqrt{n}\) is not irrational if n is a perfect square – True. (since by definition of an irrational number).
- \(\sqrt{n}\) is irrational if n is not a perfect square – True. (same as above)
- All real numbers are irrational – False (since real numbers consist of rational