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NCERT Solutions for Exercise 1.3 Class 10 Maths Chapter 1 - Real Numbers

NCERT Solutions for Exercise 1.3 Class 10 Maths Chapter 1 - Real Numbers

Edited By Ramraj Saini | Updated on Nov 02, 2023 01:21 PM IST | #CBSE Class 10th
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NCERT Solutions for Exercise 1.3 Class 10 Maths Chapter 1 - Real Numbers

This article discuss NCERT Solutions for class 10 maths ex 1.3 with all questions and answer in step by step manner. These NCERT solutions for exercise are created by expert team at Careers360 keeping in mind the need of an average students and latest syllabus of CBSE 20023-24. This exercise deals with irrational numbers which are real numbers that cannot be written in simple fractions for example π, √2, √3, √5, √7 - 3, etc. One of the theorems we use in this exercise is the Fundamental Theorem of Arithmetic.

This Story also Contains
  1. NCERT Solutions for Exercise 1.3 Class 10 Maths Chapter 1 - Real Numbers
  2. Download PDF of NCERT Solutions For Class 10 Maths Chapter 1 Exercise 1.3 Real Numbers
  3. Access Exercise 1.3 Class 10 Maths Answers
  4. Benefits of NCERT Solutions for Class 10 Maths Exercise 1.3
  5. NCERT Solutions of Class 10 Subject Wise
  6. Subject Wise NCERT Exemplar Solutions
NCERT Solutions for Exercise 1.3 Class 10 Maths Chapter 1 - Real Numbers
NCERT Solutions for Exercise 1.3 Class 10 Maths Chapter 1 - Real Numbers

There are four exercise in this chapter which are listed below. interested students can refer them and practice problems to command the concepts.

Download PDF of NCERT Solutions For Class 10 Maths Chapter 1 Exercise 1.3 Real Numbers

Download PDF

Access Exercise 1.3 Class 10 Maths Answers

Real Numbers Class 10 Chapter 1- Exercise 1.3

Q1 Prove that \sqrt 5 is irrational.

Answer:

Let us assume 5 is rational.

It means 5 can be written in the form pq where p and q are co-primes and q≠0

5=pq

Squaring both sides we obtain

(5)2=(pq)25=p2q2p2=5q2

From the above equation, we can see that p 2 is divisible by 5, Therefore p will also be divisible by 5 as 5 is a prime number. (i)

Therefore p can be written as 5r

p = 5r

p 2 = (5r) 2

5q 2 = 25r 2

q 2 = 5r 2

From the above equation, we can see that q 2 is divisible by 5, Therefore q will also be divisible by 5 as 5 is a prime number. (ii)

From (i) and (ii) we can see that both p and q are divisible by 5. This implies that p and q are not co-primes. This contradiction arises because our initial assumption that 5 is rational was wrong. Hence proved that 5 is irrational.

Q2 Prove that 3+25 is irrational.

Answer:

Let us assume 3+25 is rational.

This means 3+25 can be wriiten in the form pq where p and q are co-prime integers.

3+25=pq25=pq−35=p−3q2q

As p and q are integers p−3q2q would be rational, this contradicts the fact that 5 is irrational. This contradiction arises because our initial assumption that 3+25 is rational was wrong. Therefore 3+25 is irrational.

Q3 Prove that the following are irrationals :

(i) 1/2

Answer:

Let us assume 12 is rational.

This means 12 can be written in the form pq where p and q are co-prime integers.

12=pq2=qp

Since p and q are co-prime integers qp will be rational, this contradicts the fact that 2 is irrational. This contradiction arises because our initial assumption that 12 is rational was wrong. Therefore 12 is irrational.

Q3 (2) Prove that the following are irrationals :

(ii) 75

Answer:

Let us assume 75 is rational.

This means 75 can be written in the form pq where p and q are co-prime integers.

75=pq5=p7q

As p and q are integers p7q would be rational, this contradicts the fact that 5 is irrational. This contradiction arises because our initial assumption that 75 is rational was wrong. Therefore 75 is irrational.

Q3 (3) Prove that the following are irrationals : 6+2

Answer:

Let us assume 6+2 is rational.

This means 6+2 can be written in the form pq where p and q are co-prime integers.

6+2=pq2=pq−62=p−6qq

As p and q are integers p−6qq would be rational, this contradicts the fact that 2 is irrational. This contradiction arises because our initial assumption that 6+2 is rational was wrong. Therefore 6+2 is irrational.

Benefits of NCERT Solutions for Class 10 Maths Exercise 1.3

  • NCERT solutions for Class 10 Maths is considered the best material for 10th class maths exercise 1.3 answers.
  • NCERT Class 10th Maths chapter 1 exercise 1.3, contains all important questions from exam point of view.
  • Exercise 1.3 Class 10 Maths, is based on irrational numbers and based on the Fundamental Theorem of Arithmetic, which are important concepts of the chapter. students can also study Real Numbers Class 10 Notes to revise the concepts quickly.
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i studied 1 to 10th CBSE board abroad and 11th 12th in karnataka state board . i am a domicile of karnataka and comes under minority, income under 5 lakhs. how neet councillng will allocate my seat

Hello

Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.

1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.

2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.

3. Counseling and Seat Allocation:

After the KCET exam, you will need to participate in online counseling.

You need to select your preferred colleges and courses.

Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.

4. Required Documents :

Domicile Certificate (proof that you are a resident of Karnataka).

Income Certificate (for minority category benefits).

Marksheets (11th and 12th from the Karnataka State Board).

KCET Admit Card and Scorecard.

This process will allow you to secure a seat based on your KCET performance and your category .

check link for more details

https://medicine.careers360.com/neet-college-predictor

Hope this helps you .

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Mitali Sharma 30 January,2025
show the previous year exams ?

Hello Aspirant,  Hope your doing great,  your question was incomplete and regarding  what exam your asking.

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SWETCHCHA MISKA 10 July,2024
as an icse student in class 10 is above 80 percent good enough to get into commerce in 11th cbse

Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.

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Manasvini Gupta 23 July,2024
i had cleared 10th from cbse in 2022 2 years ago now i wish to apply for 12th as private candidate in 2025. can i do so?

hello Zaid,

Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.

best of luck!

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Ashvadha 03 July,2024
i had cleared 10th in 2022 from cbse can i apply for 12th as private candidate this year?

According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.

You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.

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