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

In this chapter, we provide KSEEB SSLC Class 9 Maths Chapter 1 Number Systems Ex 1.5 for English medium students, Which will very helpful for every student in their exams. Students can download the latest KSEEB SSLC Class 9 Maths Chapter 1 Number Systems Ex 1.5 pdf, free KSEEB SSLC Class 9 Maths Chapter 1 Number Systems Ex 1.5 pdf download. Now you will get step by step solution to each question.

Karnataka State Syllabus Class 9 Maths Chapter 1 Number Systems Ex 1.5

Karnataka Board Class 9 Maths Chapter 1 Number Systems Ex 1.5

Question 1.
Classify the following numbers as rational or irrational.
Answer:
i) 2−5–√
ii) (3+23−−√)−23−−√
iii) 27√77√
iv) 12√
v) 2π
Answer:
i) 2−5–√ = 2 – 2.2360679……….. = -0.2360679
This is a non-terminating, non-recurring decimal.
∴ This is an irrational number.

ii) (3+23−−√)−23−−√
= 3+23−−√−23−−√
= 3
⇒ 31. This can be written in the form of pq.
∴ This is a rationl number.

iii) 27√77√=27√7√=2⇒21
This can be written in the form of pq
∴ This is a rational number.

iv) 12√
12√×2√2√=2√2=1.41422
= 0.707106…………
This is a non-terminating, non-recurring decimal.
∴ This is an irrational number.

v) 2π
= 2 × 3.1415…..
= 6.2830…….
This is a non-terminating, non-recurring decimal.
∴ This is an irrational number.

Question 2.
Simplify each of the following expressions:
i) (3+3–√)(2+2–√)
ii) (3+3–√)(3−3–√)
iii) (5–√+2–√)2
iv) (5–√−2–√)(5–√+2–√)
Answer:
KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 1
KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 2

Question 3.
Recall, 2π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π=cd. This seems to contradict the fact that n is irrational. How will you resolve this contradiction?
Answer:
There is no contradiction. When we measure a length with a scale or any other device we get the quotient.
Therefore we cannot judge whether c is a rational number of d is an irrational number.
∴ Value of cd is irrational number.
∴ The value of π is also an irrational number.

Question 4.
Represent 9.3−−−√ on the number line.
Answer:
Construction: Mark the distance 9.5 units from a fixed point O such that OB = 9.3 units. Mark midpoint D of OC. Draw a semicircle with centre D. Draw a line perpendicular to OC passing through E and intersecting the semicircle at E. Draw an arc BE which intersect at F. Now, BF = 9.3−−−√.
KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 3

Question 5.
Rationalise the denominators of the following :
KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 4
Answer:
i) 17√
Denominator’s factor is 7–√ Mulitplying Numerator and denominator by 7–√.
KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 5

ii) 17√−6√
Denominator’s factor is 7–√+6–√
Multiplying numerator and denominator by 7–√+6–√,
KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 6

iii) 15√+2√
Denominator’s factor is 5–√−2–√
Multiplying numerator and denominator by 5–√−2–√.
KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 7

iv) 17√−2
Denominator’s factor is 7–√+2
Multiplying numerator and denominator by 7–√+2.
KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5 8

All Chapter KSEEB Solutions For Class 9 Maths

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All Subject KSEEB Solutions For Class 9

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