In the RD Sharma Chapter 2 Class 9 Maths Exercise 2.2 Solutions, students will get information about- Rational Exponents of Real Number, the nth root of a positive real number, Rational Powers, Laws of rational exponents in detail. For practice, students can prefer the following RD Sharma Chapter 2 Class 9 Maths Exercise 2.2 Solutions PDF, prepared by our best faculties with easy and detailed solutions.
In this Exercise 2.2 of class 9 Maths, we are providing the tricks, tips, easy formulas to solve the questions speedily. The topics are all about the square roots, cube roots, and the law to rational exponents.
Download RD Sharma Chapter 2 Class 9 Maths Exercise 2.2 Solutions PDF
Important Definitions RD Sharma Chapter 2 Class 9 Maths Exercise 2.2 Solutions
As we told above, we are providing a brief on the topics. Find the complete details in the below points with examples.
- Rational Exponents
- The nth root of a positive real number
- Laws of rational exponents
Rational Exponents are also known as “Radicals.” This includes-
- Whole Number Exponent
- Fractional Exponent
Whole Number Exponent
The exponent of a number states how many times to apply for the number in a multiplication.
- 7² = 7 × 7 = 49
- 4³ = 4 × 4 × 4 = 64
As we know, the square of power doubles the exponent. But, the fractional exponent works conversely. The square of power becomes half the exponent.
The square root of p¹ is equal to p½. In other words, p¹= √p
Similarly, the cube of power is the exponent multiplied by 3. In fractional exponent, the cube of power is the exponent divided by 3.
The cube root of
The nth root of a positive real number
The “nth Root” applied ‘n’ times in a multiplication provides the original value in which the 2nd root is the square root and the 3rd root is the cube root.
The root can be 2nd, 4th, 8th, 66th, 545th, etc., But, if we want to talk generally instead of saying like 2nd, 4th, etc. we say ‘nth’.
The symbol of ‘nth root’ is “n√” it is the radical symbol with a small ‘n’ with nth root.
Laws of Rational Exponents
Know the Laws of Rational Exponents in the below points with formulas and examples.
Multiplying of Powers with the Same Base
If the bases are the same, we need to add the exponents.
Dividing Powers with the Same Base
If the bases are the same, we need to subtract the exponent.
We need to change the negative exponent into a positive exponent first by making the numerator as the denominator and vice-versa.
Power with Exponent Zero
If the power of the exponent is zero, then the result will get ‘one’, whatever the base is.
Go through the below table to know more about the Law of Rational Exponent-