The reality
of the real numbers is introduced to in the class 10

^{th}. Though you learn the basics of the real numbers in class 9^{th}, the deeper understanding becomes possible when you study the chapter in class 10^{th}.
The
discussions of the real numbers in the ncert solutions for class
10 maths real numbers

**include different properties and algorithms related to the real numbers.**
Here, in
this article, you will find the basics of all the concepts provided in the
chapter. With the initial understanding, it will get easier to enhance your
knowledge during the chapter study.

So, let’s
dive right into it.

**1. Euclid’s Division Lemma**

The
Euclid’s division lemma is the algorithm that allows you to understand the
properties of the positive integers. You learn about the relationship between
the dividend, quotient, and remainder, which is:

· Dividend = Divisor × Quotient + Remainder

According
to Euclid’s division lemma, it is possible to get two whole numbers for the two
positive integers to form a relation:

· a = b × q + r,

· Where 0 ≤ r < b, a and b are the positive integers, q and r
are the whole numbers.

The use of
this property becomes helpful in finding the highest common factor of positive
integers. Also, the common properties of any two positive integers become
visible easily with this property.

**2. Fundamental Theorem of Arithmetic**

This
theorem provides properties of the composite numbers greater than 1. The
theorem states that every composite number, which is greater than 1, is easily
expressible as the product of two prime numbers. When it comes to the prime
factorization of a number, it is easy to write the number in the powers of its
prime factors.

The theorem
helps in finding the highest common factors and the lowest common multiple for
any two numbers. This happens due to the expression of two numbers in the form
of their prime factorization.

**3. Rational numbers**

The
identification of rational numbers becomes easier when you know how they look.
The rational numbers are written as ‘x y’, where x and y are the two integers
and y is not equal to 0.

You also
need to know the two types of the rational numbers that occur due to the
recurring or the terminating nature of the decimals.

**4. Irrational numbers**

Sometimes
the two integers are not expressible in the form of ‘x y’ the same way possible
in the rational numbers’ case. These types of numbers are called the irrational
numbers.

There are
various sub-properties related to the rational and irrational numbers that help
in calculating the solutions.

**Some important product relations between rational and irrational numbers:**

· The product of a rational and an irrational number gives an
irrational number.

· The product of two irrational numbers gives a rational or an
irrational number.

Similarly,
there are sum and difference related relations are available in the

**cbse class10 maths real numbers.**
So,
understand the real numbers to start your chapter with focused learning.

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