"What does it matter if the area of a square is 9 cm2, how does this affect me?", mumbled Billy as he did his math homework. "In lots of ways!", came an answer from the darkness outside his window. "Who said that?" shouted Billy. "It’s I, the Radical Math Hippie!" replied the voice as a scruffy figure who looked like he just got back from Woodstock climbed in the window.
"What are you doing here?", asked Billy. "I’m here to show you what you cant do with square roots!" answered the hippie.
"Like what?"
"Well if you solved the equation x2 = 9 then you would get the dimensions of the square. These could be used to make something to cover a certain area, or to help solve for a variable in a larger equation."
"Cool, but what about square roots that aren’t perfect squares?"
"Well for these problems we can use the simplest radical form of the square root. For example, root 27 (/27 ) will simplify into 3 root 3 (3/3 ). These mean that one side length is equal to 9 and the other is equal to root 3 (/3 ), because there are no perfect squares that can be removed for 3 we can leave it under the sign. Again this will let us solve for variables in a larger equation. A great example of when we use this is when trying to find the real roots for a parabola or the x-intercept of a parabola. We can then use these numbers to graph the parabola or to extract information from the equation if it represents a function of a ball or rocket for example."
"Gee, square roots are awesome Radical Math Hippie! What else can you teach me?"
"That is all I have time for tonight Billy. See you next time." And with that the Radical Math Hippie jumped out Billy’s window so he could continue his mathematical adventures.