Nth Root of a Real Number MCQs Quiz | Class 9

Test your understanding of Unit I: Number Systems for Class IX Mathematics (Code 041). This quiz covers the definition of the nth root, simplification of radicals, and related examples. Complete the questions below and click Submit to check your score and download the PDF solution sheet.

Understanding the Nth Root of a Real Number

In the Number Systems unit for Class 9, understanding radicals and exponents is fundamental. The concept of the nth root bridges the gap between powers and roots.

1. Definition

For any real number a and a positive integer n, the nth root of a is a number b such that:

b^n = a

It is denoted symbolically as:

nth root of a = a^(1/n)

2. Terminology

  • Radical Sign: The symbol used to denote the root.
  • Index (n): The small number inside the crook of the radical sign. If no number is shown, the index is understood to be 2 (square root).
  • Radicand (a): The number inside the radical sign.

3. Important Rules

Rule Name Expression Result
Product Rule nth root of (x * y) (nth root of x) * (nth root of y)
Quotient Rule nth root of (x / y) (nth root of x) / (nth root of y)
Power Rule (nth root of x)^n x

4. Examples for Revision

  • Square Root: sqrt(36) = 6 because 6^2 = 36.
  • Cube Root: cube root of 27 = 3 because 3^3 = 27.
  • Fourth Root: fourth root of 16 = 2 because 2^4 = 16.
  • Negative Base: cube root of -8 = -2 (Odd roots of negative numbers are real).

5. Extra Practice Questions

Try solving these without a calculator:

  1. Find the value of 125^(1/3).
  2. Simplify: sqrt(32) in the form k*sqrt(2).
  3. Evaluate: 81^(1/4) + 8^(1/3).
  4. Express x^(2/3) in radical notation.
  5. Calculate the value of fifth root of 243.