Operations on Real Numbers Examples
Example 1: Simplify (2√3 + √7) + (3√3 – 4√7)
Solution:
= (2√3 + √7) + (3√3 – 4√7)
= 2√3 + √7 + 3√3 – 4√7
= 2√3 + 3√3 + √7 – 4√7
= 5√3 – 3√7
Example 2: Simplify (-√3) × (- 4√3)
Solution:
= (-√3) × (- 4√3)
= 4(√3)(√3)
= 4 × 3
= 12
Example 3: Simplify (9√5 / 3√5)
Solution:
= (9√5 / 3√5)
= 9√5 / 3√5
= 3
Example 4: Simplify 34(√3) – √3(3 + √3)
Solution:
= 34(√3) – √3(3 + √3)
= 34(√3) – 3√3 – 3
= 31√3 – 3
Operations on Real Numbers
Real Numbers are those numbers that are a combination of rational numbers and irrational numbers in the number system of maths. Real Number Operations include all the arithmetic operations like addition, subtraction, multiplication, etc. that can be performed on these numbers. Besides, imaginary numbers are not real numbers. Imaginary numbers are used for defining complex numbers. To get real numbers, first, we have to understand rational numbers and irrational numbers. Rational numbers are those numbers that can be written as p/q where p is the numerator and q is the denominator and p and q are integers. For example, 5 can be written as 5/1, so it is a rational number and irrational numbers are those numbers that cannot be written in the form of p/q.
For example, √3 is an irrational number, it can be written as 1.73205081 and continuous to infinity, and it cannot be written in the form of a fraction and is a non-terminating form and non-recurring decimal. And if combine rational numbers and irrational numbers become real numbers.
Example: 12, -8, 5.60, 5/1, π(3.14), etc.
Real numbers can be positive and negative, and it is denoted by R. All the decimals, natural numbers, and fraction come under this category.