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Question 816681: can you simplify the square root of a decimal--for example the square root of 82.8--in the same way you can simplify the square root of 27?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i don't believe you are talking about simplification.
simplification means you can't perform any more operations on it, therefore the expression is simplified.
an example:
5 * (x - 3) is the expression.
when you simplify it, you perform all the operations that can be performed on it.
in this case, it to multiply it out and you get 5*x - 15.
the expression has been simplified as far as you can go since there are no more operations you can perform on it without knowing the value of x.
what you might be talking about is rounding?
when you take the square root of a number, the answer that you get is it.
there is no simplification involved.
the square root of 9 is equal to 3
the square root of 27 is equal to 5.196152423 which is the greatest accuracy that my calculator can show.
the square root of 82.8 is equal to 9.099450533 which is the greatest accuracy that my calculator can show.
if you take the square root of a number and you get an integer, then you have a perfect square.
square root of 16 is equal to 4.
square root of 25 is equal to 5.
these are all perfect squares because the square root of them is an integer.
when you do not have a perfect square, then you are dealing with a fraction or a decimal equivalent of a fraction.
for example:
2.5 squared is equal to 6.25
when you take the square root of 6.25, you will get 2.5
this number is not rounded.
it is equal to 2.5 and nothing more.
now let's take a look at 20/7 squared.
that number is equal to 8.163265306 and possible some more digits that my calculator can't show.
in terms of fractions, that number is equal to 400/49 which the 20/7 squared.
if i take the square root of 400/49, the calculator will show me that the answer is 2.857142857 and whatever other digits are to the right of that which are not being shown because the calculator can't display them all.
can i simplify that answer?
not really.
but i can try to convert it to a fraction.
i can do that manually which would be a major chore, or i can ask my calculator to do that for me.
i asked my calculator to convert that number into a fraction.
the calculator responded with:
20/7
that answer, with all the decimal points, simplifies, or reduces to 20/7
i can do that because the number is a rational number which means it is equivalent to an integer divided by another integer.
if the number was not a rational number i couldn't do that.
for example:
the square root of 2 is not a rational number because it can't be expressed as the ratio of 2 integers.
2 is a rational number because it can be expressed as 2 / 1 which is an integer divided by another integer.
square root of 2 is not a rational number because it can't.
square root of 2 is equal to 1.414213562
when i ask my calculator to convert that to a fraction, it comes back with the same decimal number which is my calculator's way of telling me that it can't convert it to a fraction.
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