Hy Friends Welcome On NCERT MATHS SOLUTIONS !! Today we are going to solve the Question : ”Use Euclid’s division lemma to show that the square of any positive integer is either of form 3m or 3m + 1 for some integer m.” of Exercise 1.1 Question No 4 Solutions (Real Numbers) of Class 10th, which will prove to be very helpful for you.
NCERT MATHS Class 10 Ex- 1.1 Q No. 4 Solutions
If you are a student of CBSE, today we are going to give you the CBSE / NCERT Chapter : Real Numbers Exercise 1.1 Question No- 4 Solutions . Hope you like this post about Class 10th Maths Solution.
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Real Numbers CHAPTER : 1
Symbol of real numbers (ℝ) In mathematics, the real number is the value presented to any amount corresponding to the simple line. Actual numbers include all rational numbers such as -5 and fractional numbers such as 4/3 and all irrational numbers such as √2 (1.41421356 …, square root of 2, an unregulated algebraic number). By incorporating the ample numbers in the actual numbers, they can be presented from the eternal points that can be attributed on a line in the form of a real number line.
Class 10 Exercise 1.1 Question No. 4 : Use Euclid’s division lemma to show that the square of any positive integer is either of 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.]
Let a be any positive integer and b = 3.
Then a = 3q +r for some integer q ≥ 0
And r = 0, 1, 2 because 0 ≤ r < 3
Therefore, a = 3q or 3q +1 or 3q + 2 or,
a2 = (3q)2 or (3q + 1)2 Or (3q + 2)2
= (3q)2 or 9q2 +6q + 1 Or 9q + 12q + 4
= 3 × (3q)2 or 3 × (3q+2q) + 1 Or 3 × (3q2 + 4q + 1) + 1
= 3k1 or 3k2 + 1 Or 3k3 +1
Where k1, k2, and k3 are some positive integers
Hence, it can be said that the square of any positive integer is either of the form 3m or 3m + 1.
CLICK ON RED BOX FOR CBSE Maths Class 10 Exercise 1 Real Numbers Next Question Answer :-
SEE NCERT Maths Class 10 Chapter 1 Ex-1.1 All Questions Solutions
- NCERT MATHS Class 10 Ex- 1.1 Q No. 1 : Use Euclid’s division algorithm to find the HCF of 135 and 225 , 196 and 38220,867 and 255
- NCERT MATHS Class 10 Ex- 1.1 Q No. 2 : Show that any positive add integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
- NCERT MATHS Class 10 Ex- 1.1 Q No. 3 : An army contingent of 616 members is to march behind an army
- NCERT MATHS Class 10 Ex- 1.1 Q No. 4 : Use Euclid’s division lemma to show that the square of any
- NCERT MATHS Class 10 Ex- 1.1 Q No. 5 : Use Euclid’s division lemma to show that the cube of any pooitive
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