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Assertion (A): . Reason (R): The cube root of a negative number is negative. Which is correct?

Class 8Cubes and Cube RootsCubes and Roots
  • ABoth A and R are true and R explains A
  • BBoth A and R are true but R does not explain A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

, so (A true). The rule means a negative number has a negative cube root (R true), and this is exactly why A holds.
Answer: A) Both A and R are true and R explains A

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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