Question

Try It!


What is the side length, s, of the square below?

A blue square labeled A equals 100 meters squared.
Each side of the square measures meters.

𝘈=𝘴𝟤=𝘴𝟤=𝗌𝟤⎯⎯⎯√±=𝘴

Convince Me!

Why are there two possible solutions to the equation, X2 = 100? Explain.

Answer 1

Solve s^2 = 100.

Algebraically s = ±√100 = ±10, because both 10^2 = 100 and (−10)^2 = 100. (You can also factor: s^2−100=(s−10)(s+10)=0 → s=10 or s=−10.)

Geometrically, a square’s side length must be nonnegative, so we reject −10 m. Therefore the side length is s = 10 meters.

Why two algebraic solutions? Squaring loses sign information: the function f(x)=x^2 is even, so x and −x give the same square. Hence x^2 = 100 has two algebraic solutions, but only the positive one is physically meaningful for a length.