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Assertion (A): −8 has no cube root among the real numbers. Reason (R): The cube of every real number is positive. Which option is correct?

Class 8Cubes and Cube RootsCubes and Roots
  • AA is false and R is false
  • BA is true and R is true, and R explains A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

A is false because , so does exist. R is false as well: the cube of a negative number is negative, e.g. . Square roots of negatives are the ones with no real value; cube roots of negatives are perfectly ordinary negative numbers.
Answer: A) A is false and R is false

Key idea: Cube root of negative integers

Cube roots of negatives are real numbers (unlike square roots).

∛ = −∛.

Example: ∛(−125). . So ∛.

This is one place where square root and cube root behave differently — square roots of negatives are NOT real (they're imaginary, a Class 11 topic). Cube roots of negatives are perfectly normal.

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