NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5.
- Number Systems Class 9 Ex 1.1
- Number Systems Class 9 Ex 1.2
- Number Systems Class 9 Ex 1.3
- Number Systems Class 9 Ex 1.4
- Number Systems Class 9 Ex 1.5
- Number Systems Class 9 Ex 1.6
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 9 |
| Subject | Maths |
| Chapter | Chapter 1 |
| Chapter Name | Number Systems |
| Exercise | Ex 1.5 |
| Number of Questions Solved | 5 |
| Category | NCERT Solutions |
NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5
Ex 1.5 Class 9 Maths Question 1.
Classify the following numbers as rational or irrational:
(1) 2-\( \sqrt { 5 }\)
(2) (3+\( \sqrt { 23 }\) )-\( \sqrt { 23 }\)
(3) \( \cfrac { 2\sqrt { 7 } }{ 7\sqrt { 7 } } \)
(4) \(\cfrac { 1 }{ \sqrt { 2 } } \)
(5) 2π
Solution:
(1) Irrational ∵ 2 is a rational number and \( \sqrt { 5 }\) is an irrational number.
∴ 2 – \( \sqrt { 5 }\) is an irrational number.
(∵ The difference of a rational number and an irrational number is irrational)
(2) 3 + \( \sqrt { 23 }\) – \( \sqrt { 23 }\) = 3 (rational)
(3) \( \cfrac { 2\sqrt { 7 } }{ 7\sqrt { 7 } } \) =\(\cfrac { 2 }{ 7 }\) (rational)
(4) \( \cfrac { 1 }{ \sqrt { 2 } } \) (irrational) ∵ 1 ≠ 0 is a rational number and \( \sqrt { 2 }\)2 ≠ 0 is an irrational a/2 number.
∴ \( \cfrac { 1 }{ \sqrt { 2 } } \) = is an irrational number.
(∵ The quotient of a non-zero rational number with an irrational number is irrational).
(5) 2π (irrational) ∵ 2 is a rational number and π is an irrational number.
∴ 2π is an irrational number, (∵ The product of a non-zero rational number with an irrational number is an irrational).
Ex 1.5 Class 9 Maths Question 2.
Simplify each of the following expressions :
(1) (3 + \( \sqrt { 3 }\) ) (2 + a/2)
(2) (3 +\( \sqrt { 3 }\) ) (3-\( \sqrt { 3 }\) )
(3) (\( \sqrt { 5 }\) + \( \sqrt { 2 }\) )2
(4) (\( \sqrt { 5 }\) – \( \sqrt { 2 }\) ) (\( \sqrt { 5 }\) + \( \sqrt { 2 }\) )
Solution:
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 = \(\cfrac { c }{ d }\). This seems to contradict the fact that it is irrational. How will you resolve this contradiction?
Solution:
Actually \(\cfrac { c }{ d }\) = \(\cfrac { 22 }{ 7 }\) which is an approximate value of π.
Ex 1.5 Class 9 Maths Question 4.
Represent \( \sqrt { 9.3 }\) on the number line.
Solution:
Mark the distance 9.3 units from a fixed point A on a given line to obtain a point B such that AB = 9.3 units. From B, mark a distance of 1 unit and mark the new point as C. Find the mid-point of AC and mark that point as O. Draw a semi-circle with center O and radius OC. Draw a line perpendicular to AC passing through B and intersecting the semi-circle at D
Then BD = \( \sqrt { 9.3 }\). To represent \( \sqrt { 9.3 }\) on the number line. Let us treat the line BC as the number line, with B as zero, C as 1, and so on. Draw an arc with center B and radius BD, which intersects the number line at point E. Then, the point E represent \( \sqrt { 9.3 }\).
Ex 1.5 Class 9 Maths Question 5.
Rationalise the denominators of the following:
(i) \( \cfrac { 1 }{ \sqrt { 7 } } \)
(ii) \(\cfrac { 1 }{ \sqrt { 7 } -\sqrt { 6 } } \)
(iii) \(\cfrac { 1 }{ \sqrt { 5 } +\sqrt { 2 } } \)
(iv) \(\cfrac { 1 }{ \sqrt { 7 } – { 2 } } \)
Solution:
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