What is the point of square roots?

Question

Why would you need to find out the square of a number? Can you give a COUPLE examples to why you would use this?

What I mean is square roots are all about being raised two 2. What makes it being raised to 2 so much better then being raised to something like 5? Why does a square of a number matter in the first place?

I'll come back and give 10 points for the best answer. I know I asked a couple of questions but if you could just answer as many as you can that would be great thanks.

Answer 1

First of all, you're confusing square roots and squares. A square of a number is the value you get when you multiply a number by itself, and a square root refers to the value that would have to be squared to get the number you started out with. In other words, 25 is the square of 5, and 5 is the square root of 25.

There are many applications in science and math where it happens that you need to multiply a number times itself, or find out what number multiplied by itself will produce the original value. They are far more numerous to mention.

One easy example is in finding the area and dimensions of shapes. Say you own a piece of land that's square in shape, and you need to put up a fence on one side. You never measured the sides, but you know it's 12,100 square feet in size. Yes, you can get out a tape measure, but it's a lot easier to take the square root of 12,100, and then go out and buy 110 feet of fence.

Here's another example. Say you manage a pizza restaurant, and the word comes down from the head office that, from now on, all pizzas must have at least one pepperoni for per square inch of pizza. You sell 7", 9" and 13" pizzas, so you need to know haw many pieces of pepperoni go on each. The area is pi * r2, where r is the radius of each pizza. For the 7", the radius would be 3.5" (half the diameter). The square of 3.5 is 12.25. Multiply by pi (3.14 is close enough for this), and the area is 38.465 square inches. You'd better be putting on 39 pepperonis, or you'll get into trouble when the company inspector comes around! (Do the math, and you need 64 pepperonis on a 9" and 133 on a 13".)

Having to raise numbers to other powers, like raising a number to the 5th power, don't come up as often, partly because we live in a three-dimensional world, and often have to deal with only two of those dimensions at a time. Numbers to the third power and cubed roots are common, though, too. It's not that squares and square roots are "better" than other powers, it's just that they get used more often. The less complicated the task, the more likely to be dealing with squares and square roots instead of large powers.

Answer 2

Your question to mathematicians would be a kind of blasphemy.

But you are right, maybe sometimes we need to stop and to think: What is the usefulness of this stuff?

I just have an historical explanation based in the measurement of lands in the ancient cultures. They always need to know what was the lenght of the side of a landing fo agricultural purposes.

The figure that guarantees the maximun area with less perimeter is the "square" so, if a landing should be divided in squared areas,it was necessary to know the lenght of the side and the only way to know it was extracting "square roots"(although in those times people did not use the concept as currently we conceived it. For them was just the knowledge of a geometric property of a figure not an abstract entity).

I can teel you that may be that is the reason that extracting the "square root" of a number is more "familiar" or useful than extracting "cubic", "fourth", "fifth", etc, root.

Hope this was useful to you.

Good luck!

Answer 3

Because geometry, being so important to us in science and engineering and archtiecture, involves a lof of quantities that are square roots of something else. Such as use of the Pythagorean formula for the hypotenuse.

Rereading your question again, which I think is confusing (are you objecting to square roots or squares?), I will try to give a more general answer to both. It turns out that of all the exponentials used in math and science, the square root and square are by far the most frequently used. It appears everywhere you go. For example, when analyzing falling bodies and rocket trajectories, the square and the square root pops up everywhere. You rarely ever see anything else like cubes and cube roots in this subject. Even Einstein's famous equations in Special Relativity only have squares and square roots, there are no cubes and cube roots, or anything else like that. If you want an answer why this should be so, see my original answer above. A lot of things that we analyze are actually geometric in nature, and geometry is full of them. For example, all conic curves such as circles, ellipses, hyperbolas, parabolas, are described with equations containing only squares and square roots (which is why they're called 2nd order curves), and distances between intersections of any combination of lines, circles, ellipses, hyperbolas are frequently expressed in those terms as well. Need I get into trignometry to show more examples?

Answer 4

here's an example
let's say you are trying to find how much water runs through a pipe, knowing how fast it travels.
to get this flow you would have to multiply this speed with the section area of the pipe.
if the pipe is round (most are) then how do you calculate it?
you take a measuring tape, you put it around the pipe and get the circumference. or, if you have the means you can determine the diameter of the pipe.
but to get to the section area you have to use a formula, which is the circle area formula.
A = PI * R2
where PI is the circumference divided by the diameter.
this is one case where you must use a power.
if you consider the opposite case, when you know the volume of water that runs through the pipe and want to determine how big the pipe should be.
for example an engineer needs to build a pipe that can transport a certain volume of water. since the water can't travel over a certain speed through the pipe, due to material limitations and various flow phenomena, this means that it has to meet a specific diameter.
so he takes the maximum speed of the water and divides the flow by that speed resulting the section area of the pipe. with this he'll easily find how large should the pipe be:
R = square root (A / PI)

Answer 5

Since it is given the name the square, it must have struck the inventor the area of square which is nothing but side * side which is also represented as side^2 so he/she would have thought it would be better to give in powers of 2 rather than powers of 5. It is necessary to find the square of a number whenever you use or apply the pythagoras theorem.For example
DATA GIVEN sin theta=3/5 find cos theta
In this u hv to find the adjacent side in order to find the cos theta,
here u hv to use the square,then subtract the two and take square root inorder to get the adjacent side.
ie: adjacent=[(5^2)-(3^2)]^(1/2) = 4
therefore cos theta=4/5.

Answer 6

John has five children. Each of his five children also have five children. How many grandchildren has John?

You are a hacker. You want to find somebody's PIN. It is four digits, and digits can be repeated. How many possibilities are there for this person's PIN?

You're tiling a floor. The room size is 8' * 8'. Each tile is 9" by 9". How many tiles need you purchase?

Answer 7

They are very important in geometry (surveying) and show up all the time in calculations for physics, chemistry and engineering. Without them you wouldn't have the engineering that designed your computer,your TV or your iPOD.

Answer 8

It's easier to write 2^16 than (2)*(2)*(2)*(2)*(2)*(2)*(2)*(2)*(2)*(2)*(2)*(2)*(2)*(2)

It's used for grouping

Answer 9

I dont know but it must have made sense to the person who thought of them