Is 25cm^2 square rooted equal 5 cm, or does it just equal 25 cm?

Question

I'm a little confused because I always thought that a square root simply cancels a square without bothering the number (radical), but from on example 3, they say otherwise. So I'm just checking because I'm a bit confused. @_@ Help please~

& thanks a lot to everyone who does!

So does that mean this website on Example 3 http://www.mathgoodies.com/lessons/vol2/circle_area.html is wrong?

Answer 1

The square root of (25^2) does equal 25. The cube root of (25^2) equals 5.

Answer 2

Your notation "25cm^2 square rooted" is nonstandard. If that's supposed to mean the square root of 25 square centimeters, the answer is 5 centimeters and that's that.

Otherwise you've got some notational problems.

When you come across something that's nonstandard and has no parenthesis, you have to use a mixture of common sense, convention, and the priority rules.

By convention, putting a number next to a unit creates an implied multiplication, and exponential functions like squaring take precedence over multiplication and division. Therefore, 25cm^2 expands out to 25 * (cm^2).

Thare are three ways to resolve the awkward use of the English phrase rather than mathetmatical expression for "square rooted." First, it only applies to the 2. So you have 25 * (cm ^ ( 2 ^ 0.5)). Fractional dimensions are possible in fractals and quantum mechanics, but I doubt we're doing either here so this answer defies common sense.

The second possibility is that square rooted applies to both "cm" and "^2" -- but not the 25. In other words, 25 * ((cm ^ 2) ^ 0.5), which is indeed 25 cm. But it's arbitrary to draw implied parentheses around two out of three parts of the expression.

The third and best is as stated above, that "square rooted" applies to the entire mathematical expression. It seems reasonable that any operator described by English expression rather than mathematical symbols applies to the entire symbolic expression it is next to. Moreover, this is the only possibility that is neither arbitrary nor produces fractional dimensions.

You do have to watch your parentheses and units in complex calculations. There are some instances where you might be taking the square root of part of an expression, not the full expression. So see what is inside the parenthesis, or if you're using old-style notation, what is inside the bar part of the square root symbol.

Answer 3

If you are saying:

sqrt(25 ^2) then yes, the answer is 25

but if you are saying what is the dimension of a square that is 25cm^2, then the size of the square is 5cm by 5cm.

In the above case, ^2 is part of the unit, not the formula.

You have to go back and re-read the question.

Answer 4

square root of 25^2 is 25.
bu the square root of 25 cm^2 is 5 cm.

Notice where the ^2 is in both examples?

Answer 5

the square root of 25cm^2 = 5 cm

The example 3 in that website is correct.

Note: (5cm)^2 = 5^2cm^2 = 25cm^2

Answer 6

they say 25 cm^2 as an area. the units are "cm^2"
so its 25 (cm^2) not (25cm)^2.
so if u take the square root, its sqrt (25 [cm^2]), which is equal to:
sqrt(25)sqrt(cm^2)
=5 cm

hope that kinda helps.
so if they say the area of the rectangle is 25cm^2, it means that the units are "cm^2". hope that helps

Answer 7

25 square cm is equivalent to the area of a figure, like a square 5 cm on each side....

The square root physically results in one side of the square: 5 cm

Units and number - that's how it works - and that's where the term "squared" originates.

Answer 8

the root of(25 cm^2) is 5 cm. the radical cancels cm^2 to cm. and the radical cancels 25 which is 5^2 to 5.

Answer 9

25 cm
the square root of a number square does cancel the square

Answer 10

it's 25 because when you square a number and then square root it you're right back to where you started, same with square rooting it and then squaring it, because square roots and squares are opposites***But that example never says anything about the squae root of it, at least from what i interpreted.