MP Board Class 9 Maths Solutions Chapter 1 Number System Ex 1.2

In this article we have given MP Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.2 with pdf.

BoardMadhya Pradesh
Class9th
SubjectMathematic
Chapter 1 Number System Exercise 1.2
MP Board Solutions for Class 9

MP Board Solutions Class 9th Maths Systems Exercise 1.2

Question 1.
State whether the following statements are true or false. Justify your answers.

  1. Every irrational number is a real number.
  2. Every point on the number line is of the form √m , where m is a natural number.
  3. Every real number is an irrational number.

Solutions:

  1. True, because all irrational numbers come in the collection of real numbers.
  2. False, because a negative number cannot be the square root of any natural number.
  3. False, because the collection of real numbers contains not only irrational numbers but also rational numbers.

Question 2.
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.
Solution:
No. For example, √4 = 2 is a rational number.

Question 3.
Show how √5 can be represented on the number line.
Solution:
Representing √5 on a number line as shown in fig. below.

MP Board 9th Maths Exercise 1.2 Question 3 Solution
MP Board 9th Maths Exercise 1.2
  1. Take OA = 2 units and draw perpendicular AB on A.
  2. Cut AB = 1 unit and join OB.
  3. By taking O as centre and OB as radius, draw an arc which inter-sect the number line at C.

Hence OC = √5
∴ Point C represents ^5 on the number line.
Proof:
OBD is a right angled A.
∴ OD2 = OB2 + BD2
OD2 = (2)2 + (1)2 = 5
OD = √5

MP Board 9th Maths Exercise 1.2 Question 3 Solution 2
Representation of Real Numbers on Number Line

Real Numbers:
The rational and irrational numbers taken together are known as real numbers. Every real number Is either rational or irrational. Different operations on real numbers are shown below:
For example:

Example 1.
Add (3√2 + 5√3) and (√2 + √3).
Solution:
(3√2+ 5√5)+ (√2+ √3)
= 3√2 + 5√5 + √5 + √5 = (3√5+ √5)+ (5√5+ √5)
= 4√2 + 6√3
= 4√5 + 6√5

Example 2.
Add (√5 + 7√5) and (4√3 + 6√5).
Solution:
(√5 + 7√5) + (4√3 + 6√5)
= √3 + 7√5 + 4√3 + 6√5
= (√3 + 4√3) + (7√5 + 6√5)
= 5√3 + 13√5.

Example 3.
Simplify (3 + √2) (3 – √2).
Solution:
(3)2 – (√2)2
(∴ a2 – b2 = (a + b) (a – b))
= 9 – 2
= 7.

Example 4.
Divide 16√6 by 4√2 .
Solution:
16√6 ÷ 4√2
166√42√
4√3.

Example 5.
Simplify the following:

MP Board 9th Maths Exercise 1.2 Example 5

Solutions:

MP Board Class 9 Maths Exercise 1.2 Example 5 Solution (i)
MP Board 9th Maaths Exercise 1.2 Question 5 Solution (ii)
MP Board 9th Maths Exercise 1.2 Example 5 Solution (iv)

Example 6.
Simplify by rationalising the denominator of MP Board 9th Maths Exercise 1.2 Example 6

Solution:
We have 3 MP Board 9th Maths Exercise 1.2 Example 6 multiply numerator and denominator by 2 + 3√5, we have

MP Board 9th Maths Exercise 1.2 Example 6 Solution

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