**NCERT/CBSE MATHS Class 10 Ex- 1.1 Q No. 5 Solutions : Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m +1m or 9m + 8.**

Hy Friends Welcome On **NCERT MATHS SOLUTIONS** !! Today we are going to solve the Question : **”Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m +1m or 9m + 8.” **of** Exercise 1.1 Question No 5 Solutions (Real Numbers)** of Class 10th, which will prove to be very helpful for you.

# CBSE/NCERT MATHS Class 10 Ex- 1.1 Q No. 5 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- 5** **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.

**Exercise 1.1 Question No. 5 : **Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m +1mor 9m + 8.

**Class 10 Exercise 1.1 Question No. 5 Solutions**

Let a be any positive integer and b = 3

a = 3q + r where q ≥ 0 and 0 ≤ r < 3

a = 3q or 3q + 1 or 3q + 2

Therefore, every number can be represented as these three forms.

There are three cases.

**Case 1:** When a = 3q,

a^{3} = (3q)^{3} = 27q^{3} = 9 (3q^{3}) = 9q^{3}

Where m is an integer such that m = 3q^{3}

^{ }**Case 2**: When a = 3q + 1,

a^{3} = (3q + 1)^{3}

a^{3} = 27q^{3} + 27q^{2} + 9q +1

a^{3} = 9 (3q^{3} + 3q^{2} + q) +1

a^{3} = 9m +1

Where m is an integer such that m = (3q^{3} + 3q + q)

**Case 3:** When a = 3q + 2,

a^{3} = (3q +2)^{ 3}

a^{3 }= 27q^{3} + 54q^{2} + 36q + 8

a^{3} = 9 (3q^{3} + 6q^{2} + 4q) + 8

a^{3} = 9m + 8

Where m is an integer such that m = (3q^{3} + 6q^{2} + 4q)

Therefore, the cube of any positive integer is of the form 9m, 9m + 1, or 9m + 8.

**CLICK ON RED BOX FOR CBSE Maths Class 10 Exercise 1.2 Real Numbers Next Question Answer :-**

**NCERT MATHS Class 10 Ex- 1.2 Q No. 1 : Express each number as product of its prime factors : 140,156**

**SEE NCERT Maths Class 10 Chapter 1 Ex-1.1 All Questions Solutions **

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