# Real Numbers

REAL NUMBERS#1- INTRODUCTION – CLASS XTH MATHS CBSE -(IN HINDI)

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REAL NUMBERS#2 EX 1.1 – Finding HCF using Euclid’s Division Lemma, CBSE CLASS 10 MATHS in HINDI

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Real Numbers#3 EX1.1 – Q.No 3, EXAMPLE 4 – CLASS 10 MATHS CBSE in Hindi

Real Number EX1.1 – Q.No 3, EXAMPLE 4 (Application Of Euclid’s Division Lemma) – CLASS 10 MATHS CBSE in Hindi.
In this video we have discussed two questions based on application of Euclid’s Division Lemma from the chapter Real Numbers CBSE class 10 mathematics. The two questions which have been discussed here are:

Example 4 : A sweetseller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the maximum number of barfis that can be placed in each stack for this purpose?
EXERCISE 1.1
3. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
Visit our official website http://www.onlinepsa.in for more videos on class 10 mathematics.

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Real Numbers#4 EX 1.1 – Q.No 2,4,5 – CLASS 10 MATHS CBSE (in Hindi)

This is the 4th video of the series Real Numbers in which we have discussed Question number 2,4 and 5 from exercise 1.1. These questions are very important in terms of examination point of view and out of these three similar type of questions you can expect one guaranteed question in board examination. So dont forget to watch the video completely.

EXERCISE 1.1
2. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
4. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. [Hint : Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square each of these and show that they can be rewritten in the form 3m or 3m + 1.]
5. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

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Real numbers#5 Ex1.2 (Q.No-1,2,3,4) CBSE CLASS 10 MATHS (in HINDI)

Real numbers#5 Ex1.2 (Q.No-1,2,3,4) CBSE CLASS 10 MATHS NCERT SOLVED AND EXPLAINED in Hindi.
In this video we have discussed Q.No- 1,2,3,4 from EX1.2 of chapter 1 Real numbers. Following Questions have been discussed in this video which are basically finding HCF and LCM using the concept of Euclid’s Division Lemma/algorithm.

EXERCISE 1.2
1. Express each number as a product of its prime factors:
(i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429
2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.
(i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54
3. Find the LCM and HCF of the following integers by applying the prime factorisation method.
(i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25
4. Given that HCF (306, 657) = 9, find LCM (306, 657).

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Real numbers#6 Ex1.2 (Q.No-5,6,7) CBSE CLASS 10 MATHS in Hindi

Real numbers#6 Ex 1.2 (Q.No-5,6,7) CBSE CLASS 10 MATH (in Hindi-Eng)
In this video we have discussed Q.No- 5,6,7 from EX 1.2 of chapter 1 Real numbers. Following Questions have been discussed in this video which are basically application based question from the concept of Euclid’s Division Lemma/algorithm and Fundamental Theorem of Arithmetic.

EXERCISE 1.2
5. Check whether 6^n can end with the digit 0 for any natural number n.
6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
7. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes
will they meet again at the starting point?

visit our official website for more videos on CBSE class 10 maths http://www.onlinepsa.in

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Real numbers#7- Ex1.3 – Root 2 is Irrational, CBSE class 10 MATHS

In this video we have explained some concepts from the chapter “Real Numbers – CBSE CLASS 10 ” which are particularly required to prove the irrationality of root 2.

The concepts discussed in this video are –
1. what are irrational numbers?
2. what are co-prime numbers?
3. Theorem 1.3: which states that “Let p be a prime number. If p divides a-square, then p divides a, where a is a positive integer.”
-Prove that root 2 is irrational.
– Prove that root 5 is irrational.

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# REAL NUMBERS#8 EX 1.3 (Q.No- 2,3 EXPLAINED) , CBSE CLASS 10 MATH (in Hindi)

In this video we have discussed Q.No 2 & 3 from the Exercise 1.3 of chapter “REAL NUMBERS” class 10 cbse. This video is the continuation part of our previous video on Real numbers#7- Ex1.3 – Root 2 is Irrational, CBSE class 10 MATHS where we have discussed about “PROVING IRRATIONALITY” .

Exercise 1.3

2. Prove that 3 + (2root5) is irrational.
3. Prove that the following are irrationals :
(i) 1/(root2)
(ii) 7(root5) (iii) 6 +(root2)

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# Real Numbers#9 Ex 1.4 – Class 10 Math CBSE (in Hindi)

This is the last video for the chapter Real Numbers cbse class 10. In this video, we have discussed the trick to recognize whether the rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion without actually doing long division .

Following concepts have been discussed in this video:
Theorem1.7 : Let x =p/q be a rational number, such that the prime factorisation of q is not of the form 2^n5^m, where n, m are non-negative integers. Then, x has a decimal expansion which is non-terminating repeating (recurring).

Exercise 1.4

1. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion.

2. Write down the decimal expansions of those rational numbers in Question 1 which have terminating decimal expansions.

3. The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If, they are rational, and of the form , what can you say about the prime factors of q?
(i) 43.123456789

(ii) 0.1201120012000120000…

(iii)43.123456789 (complete bar after decimal)