Class 9 Exam  >  Class 9 Notes  >  Mathematics (Maths) Class 9  >  HOTS Questions: Number System

Class 9 Maths Chapter 1 HOTS Questions - Number System

Q1. Find the value of:

√32 + √48√8 + √12

Solution: Since,

√32 = √16 × 2 = 4√2 ; √48 = √16 × 3 = 4√3

Similarly, √8 = √4 × 2 = 2√2 and √12 = √4 × 3 = 2√3

Therefore, 4√2 + 4√32√2 + 2√3 = 4(√2 + √3)2(√2 + √3) = 2

Q2. If √2 = 1.4142, then find the value of:

√2 − 1√2 + 1

Solution:

Rationalising the denominator of: √2 − 1√2 + 1

√2 − 1√2 + 1 × √2 − 1√2 − 1 = (√2 − 1)2(√2)2 − (1)2

= (√2 − 1)22 − 1 = (√2 − 1)2

√2 − 1√2 + 1 = √2 − 1

Substitute √2 = 1.4142:
1.4142 − 1 = 0.4142

Q3. Find the value of 'a' in:

3 − √53 + 2√5 = a√5 − 1911

Solution:

L.H.S: 3 − √53 + 2√5 × 3 − 2√53 − 2√5 (Rationalising the denominator)

= 9 − 6√5 − 3√5 + 10(3)2 − (2√5)2 (Using (a + b)(a − b) = a2 − b2)

= 19 − 9√59 − 20 = 19 − 9√5−11 = 9√5 − 1911

So, L.H.S = R.H.S

i.e. 911 √5 − 1911 = a√5 − 1911

⇒ a = 911

Q4. Find the value of 'a' and 'b':

7 + √57 − √57 − √57 + √5 = a + 711 √5 b

Solution:

L.H.S: 7 + √57 − √57 − √57 + √5

= (7 + √5)2 − (7 − √5)2(7 − √5)(7 + √5) = 49 + 5 + 14√5 − 49 − 5 + 14√549 − 5

= 4 × 7√544 = 7√511

So, L.H.S = R.H.S

R.H.S = a + 711 √5 b

Since, L.H.S = R.H.S

∴ 0 + 711 √5 = a + 711 √5 b

⇒ a = 0, b = 1

Q5. If a = 3 + √52 , then find the value of a² + 1

Solution:

a = 3 + √521a = 23 + √5

Now, a² + 1/a² = (a + 1/a)² − 2

⇒ a² + 1/a² = (3 + √5)/2 + 2/(3 + √5)1 − 2

= [(3 + √5)² + 2²]2(3 + √5) − 2

= 9 + 5 + 2 × 3 × √5 + 42 × 3 + 2 × √5 − 2

= 18 + 6√56 + 2√5 − 2

= (6(3 + √5))²(2(3 + √5))² − 2

= (6/2)²9 − 2

= 3² − 2 = 7

So, a² + 1 = 7.

The document Class 9 Maths Chapter 1 HOTS Questions - Number System is a part of the Class 9 Course Mathematics (Maths) Class 9.
All you need of Class 9 at this link: Class 9
Are you preparing for Class 9 Exam? Then you should check out the best video lectures, notes, free mock test series, crash course and much more provided by EduRev. You also get your detailed analysis and report cards along with 24x7 doubt solving for you to excel in Class 9 exam. So join EduRev now and revolutionise the way you learn!
Sign up for Free Download App for Free
45 videos|412 docs|53 tests

Up next

FAQs on Class 9 Maths Chapter 1 HOTS Questions - Number System

1. What is the number system?
Ans. The number system is a way of representing numbers using symbols or digits. It consists of different sets of numbers such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
2. What are natural numbers?
Ans. Natural numbers are a set of numbers that starts from 1 and goes on infinitely. They are also known as counting numbers and do not include zero or any negative numbers.
3. What are rational numbers?
Ans. Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. They can be positive, negative, or zero and include numbers like 1/2, -3/4, and 0.
4. What are irrational numbers?
Ans. Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They are non-repeating and non-terminating decimals. Examples of irrational numbers include π (pi) and √2 (square root of 2).
5. What is the difference between whole numbers and integers?
Ans. Whole numbers include all the natural numbers along with zero, whereas integers include all the whole numbers along with their negative counterparts. In other words, integers are a superset of whole numbers, as they include both positive and negative numbers.
45 videos|412 docs|53 tests
Download as PDF

Up next

Explore Courses for Class 9 exam
Related Searches

Objective type Questions

,

Class 9 Maths Chapter 1 HOTS Questions - Number System

,

practice quizzes

,

shortcuts and tricks

,

study material

,

Viva Questions

,

Extra Questions

,

ppt

,

Class 9 Maths Chapter 1 HOTS Questions - Number System

,

past year papers

,

MCQs

,

Free

,

Semester Notes

,

Important questions

,

Summary

,

Exam

,

video lectures

,

mock tests for examination

,

pdf

,

Class 9 Maths Chapter 1 HOTS Questions - Number System

,

Sample Paper

,

Previous Year Questions with Solutions

;