Question

Charles wants to compare the solutions to the equations x^2=64 and x^3=64.

Compare the signs of the solutions. Explain your reasoning.

Answer 1

x = ±4

x = 4

Explanation:

x² = 64.

Square root both sides

√x² =√64

x= ±8

When squaring both sides, the required solution is both positive and negative since the product of two negative number is positive.

x³ = 63.

Cube root both sides

3√x³ = 3√65

x =4

This only gives a positive number not negative since the product of three negative number gives a negative number