Question

How does finding the square root of a number compare to finding the cube root of a number? Use the number 64 in your explanation.

Answer 1

square-root:
\[x^2=64\\
x^2-64=0\\
(x-8)(x+8)=0\\
x-8=0\qquad x+8=0\\
x=8\qquad x=-8\]
cube-root:
\[x^3=64\\
x^3-64=0\\
(x-4)(x^2+4x+16)=0\\
x-4=0\qquad x^2+4x+16=0\\
x=4\qquad\qquad\text{no real roots here}
\]