Question

What calculation can be used to find the value of p in the equation p^3 =8

Answer 1

Cube Root

${p}^{3} = 8 \\ p = \sqrt[3]{8} \\ p = \sqrt[3]{ 2\times 2 \times 2} \\ p = 2$

Formula

${p}^{3} - 8 = 0$

Use the following formula.

${x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )$

$(p - 2)( {p}^{2} + 2p + 4)$

The expression p²+2p+4 has the discriminant less than 0 ( D < 0 ).

Thus, remove the expression and leave only p-2

$p - 2 = 0 \\ p = 2$

Substitution

The most obvious number that multiplies itself three times and equal 8 is 2.

Substitute p = 2

${p}^{3} = 8 \\ {2}^{3} = 8 \\ 2 \times 2 \times 2 = 8 \\ 8 = 8$

The equation is true, thus 2 is the answer.