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By how much does the cube of 6 exceed the square of 6?

Class 8Cubes and Cube RootsCubes and Roots
  • A150
  • B36
  • C180
  • D210

Step-by-Step Solution

and , so the excess is 216 − 36 = 180. Answering 36 reports the square itself instead of the difference.
Answer: C) 180

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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