Where do you need or use square roots?
- and where do you need algebra

Students ask: Why do I need to know how to calculate the square root of a number? What is the why calculate square root - beyond (or behind) it is used in math formulas? Are square roots really needed in life outside just math studies?

Here's an idea of how you as a teacher/parent can at the same time show students one important real-life application of square root AND let them ponder where math is needed AND hopefully pique their interest into math problems in general. This lesson idea will work best when you've taught the square root concept but not yet touched on Pythagorean theorem.

• Draw a square on board/on paper and draw one diagonal into it. Make the sides of the square to be, say, 5. Then make the picture to be a right triangle by wiping out the two sides of square. Then ask students how to find the length of the longest side of the triangle.
  
  Of course you realize the students probably can't find the length - if you haven't yet studied Pythagorean theorem. But that's part of the 'game'. Have you ever seen ads where you couldn't tell what they were advertising? Then in few weeks the ads change and 'reveal' what it is all about. It makes you curious, doesn't it.
  
  So try let them think about it for a few minutes and not tell them answer. It might pique their interest a lot... Soon you'll probably study Pythagorean theorem anyway, since in schoolbooks it often follows square root.
   
• Then go on to the question: where would that kind of calculation be needed? In what occupations or situations would you need to find the longest side of a right triangle if you know the sides? This can get them to thinking and involved!
  
  The answer would be any kind of occupation or trade that involves triangles like carpenters, engineers, construction workers, those measuring and marking land, artists, designers of many sorts.
  
  I've observed people laying block who needed to first measure and mark on ground exactly where the building would go. Well they had the sides and they went with the tape measure to measure the diagonals and were asking ME what the measure should be because they couldn't quite remember but were wishing for better knowledge of the matter. This diagonal check is to ensure it's really going to be a rectangle and not a parallelogram. It's not easy to 'draw' a right angle when doing things on ground itself. In fact you usually don't even try to draw a right angle but use different kinds of triangle check points to make sure you got your angle as right angle.

Then, beyond this simple example, square root as a CONCEPT is needed to understand other math concepts and to study math further. Studying math is like building a block wall or building: you need the blocks on the lower part to build on, and if you leave holes in your building, you can't build on the hole.

So, you can mention to your students that the concept of square root is a prerequisite and ties in with many many other math concepts:

• square root → 2nd degree equations → functions & graphing
• square root → Pythagorean theorem → trigonometry
• square root → fractional exponents → functions & graphing
• square root → irrational numbers → real numbers

there are probably more examples that I didn't think of for right now. If you do, please send them in!

This all may lead the youngsters to ask:

Where do you need trig and algebra?

The answer to that is that in many many fields and occupations that require higher education like computer science, electronics, engineering, medicine (doctors), trade and commerce analysts, ALL scientists, etc. In short, if someone is even considering higher education, they should study algebra.

Algebra also develops thinking skills and problem solving skills. And, it is needed to take your SAT test.

Then you can admit to your student(s) that yes, square roots are not needed in every single occupation, those of mostly manual labor for example. That is no big secret; kids know that. But try to ask them that do they know for sure what they are going to become as adults? Most kids in middle school are not sure at all. If they are not sure, they better study all school subjects and learn all they can so that when they finally have some idea, they won't be stopped because of not having studied and understood square roots.

And, even if they think they know what they want to be, how many times have young people changed their mind?? Even we as adults don't necessarily know what kind of job or career changes are awaiting us. In times past, you could pretty well bank on either becoming a housewife (girl), or continuing in your father's occupation (boy). In today's world this is not so. Kids have more freedom in choosing - but the other side is that young people need to study more to get a good solid basic education. Sometimes young people just need an adult to tell them about these things: they don't know all about their future so they need to keep studying, even math.

See also

Math Careers Database - descriptions for 277 major jobs and what math topics are needed on the job.

Why study mathematics? From A Home for Homeschoolers

Algebra in the Real World
Short movies, lesson guides, and student worksheets that tie algebra in with real word applications, such as roller coasters, banking, rice production, skyscrapers, solar power, and lots more.

Mathematical Moments - a series of one-page PDF files that promote appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture. The one-page flyers cover very diverse topics such as findign oil, solving crimes, DNA, brain, traffic, aircraft design, etc.

Where do you need exponents in everyday life?

Math. "How am I ever going to use this stuff?"A great collection of REAL-world math problems contributed by a variety of businesses, demonstrating the relevance of math in today's world. The intent of these lessons is to excite students about mathematics, to expose students to professions that employ mathematics, and to demonstrate the relevance of mathematics in solving real-world challenges.

Why Do I Need to Know Math? Who needs this stuff anyway?
What have others asked and answered about the importance of studying algebra? Math on the Job and Professional Profiles.

Career profiles
Essays from authors from a variety of careers for which a background in the mathematical sciences is useful.

Examining How Mathematics is Used in the Workplace
Mathematics in Automobile Production; Proportional Reasoning by Nurses; Modeling the Mathematics of Banking; Mathematical Models as Seen by Biologists; How do Scientists Interpret Graphs?

Career profiles in mathematical sciences
If you were a math major, what kind of jobs could you end up with?

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