Cube Root Formula

The cube of any number is found by multiplying the number three times. For example – 5 $\times$ 5 $\times$ 5 = 125.

The cube root formula is the vice versa of the cube formula. Check the example below for detail –

5 cube = \(5^{3}\) = $125$
Cube Root of 125 = $\sqrt[3]{125}$ = $5$

Thus, cube root of 125 is 5. The number 125 is a perfect cube.

Cubes of some number are as follows –

$1^{3}$ = $1$
$2^{3}$ = $8$
$3^{3}$ = $27$
$4^{3}$ = $64$
$5^{3}$ = $125$
$6^{3}$ = $216$
$7^{3}$ = $343$
$8^{3}$ = $512$
$9^{3}$ = $729$
$10^{3}$ = $1000$

Solved Examples

Question 1: What is the cube root of 1728?
Solution:

The factors of 1728 are given as,

1728 = 12 $\times$ 12 $\times$ 12

$\sqrt[3]{1728}$ = $\sqrt[3]{12 \times 12 \times 12}$

$\sqrt[3]{1728}$ = 12


Practise This Question

The enthalpies for the following reactions at 25°C are given.
12 H2(g) + 12 O2(g)OH(g); H = 10.06 K cal
H2(g)2H(g); H = 104.18 K cal
O2(g)2O(g); H = 118.32 K cal

Calculate the OH bond energy in the O - H group