Find the cube root of $1728$ . Write the answer as an integer.

easy 1 mark Class 8 · Mathematics · Cubes and Cube Roots

Answer

The correct answer is 12 — Thus the integer cube root is $12$ .

Step-by-step solution

Determine that $1728$ can be expressed as $1 2^{3}$ by factorising it into prime factors $2^{6} c d o t 3^{3}$ and observing that $(2^{2} c d o t 3)^{3} = 1 2^{3}$ .
Take the cube root of both sides to get $s q r t [3] 1728 = 12$ .
Thus the integer cube root is $12$ .

Common mistake: Failing to recognise that

1728

equals

1 2^{3}

and computing an incorrect root.

Concept tested: Cube root calculation