NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 are the part of NCERT Solutions for Class 9 Maths. Here you can find the NCERT Solutions for Class 9 Maths Chapter 1 Number System Ex 1.5.



Ex 1.5 Class 9 Maths Question 1.
Classify the following numbers as rational or irrational.


Solution:
(i)
The difference between a rational number and an irrational number is always an irrational number.
2 – √5 is an irrational number.
(ii) (3 + 23) – 23 = 3 + 23 – 23 = 3
Here, 3 is a rational number. Thus, (3 + 23) – 23 is a rational number.
(iii) Since, 27/77 = 2/7, which is a rational number. Therefore, 27/77 is a rational number.
(iv)
The numerator is a rational number and the denominator is an irrational number. The quotient of a rational divided by an irrational number is an irrational number.
 1/2 is an irrational number.
(v)
2π = 2 × π = Product of a rational number and an irrational number is an irrational number.
2π is an irrational number.

 

Ex 1.5 Class 9 Maths Question 2.
Simplify each of the following expressions.


Solution:
(i)
(3 + √3)(2 + √2)
= 3(2 + √2) + √3(2 + √2)
= 6 + 3√2 + 2√3 + √6
Thus, (3 + √3)(2 + √2) = 6 + 3√2 + 2√3 + √6
(ii) (3 + √3)(3 – √3) = (3)2 – (√3)2
                                  = 9 – 3 = 6
Thus, (3 + √3)(3 – √3) = 6
(iii) (√5 + √2)2 = (√5)2 + (√2)2 + 2(√5)(√2)
                         = 5 + 2 + 2√10 = 7 + 2√10
Thus, (√5 + √2)2 = 7 + 2√10
(iv) (√5 – √2)(√5 + √2) = (√5)2 – (√2)2 

                                       = 5 – 2 = 3
Thus, (√5 – √2) (√5 + √2) = 3

 

Ex 1.5 Class 9 Maths Question 3.
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is π = c/d. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

Solution:
When we measure the length of a line with a scale or with any other device, we only get an approximate rational value, i.e., c and d both are approximate rational value.
 c/d is irrational and hence π is irrational.
Thus, there is no contradiction in saying that π is irrational.

 

Ex 1.5 Class 9 Maths Question 4.
Represent 9.3 on the number line.

Solution:
Draw a line segment AB = 9.3 units and extend it to C such that BC = 1 unit.
Find the mid-point of AC by bisecting the line segment AC and mark it as O.
Draw a semicircle taking O as centre and AO or OC as radius. Draw BD
AC.
Draw an arc taking B as centre and BD as radius meeting AC produced at E.

Now, BE = BD = 9.3 units


Ex 1.5 Class 9 Maths Question 5.

Rationalise the denominators of the following:


Solution:


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