NCERT Solutions for Class 10 Chapter 1 Real numbers

Video solutions for Real Numbers

## NCERT Solutions for Class 10 Chapter 1 Real numbers Exercise 1.1 Q4

Extra Questions For Real Numbers

NCERT Solutions for Class 10 Chapter 1 Real numbers Exercise 1.1 Q4

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.]

Solution:

Let x be any positive integer and b=3.

According to Euclid’s division lemma, we can say that

Let be some integer, we get

Case 2:

Let be some integer, we get

Case 3:

Let be some integer, we get

Hence, square of any positive integer is either of the form 3m or 3m+1 for some integer m.

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