How do you simplify #1000^2/(252^2 - 248^2)# ?

Question

Isaiah Anthony · Accepted Answer

#1000^2/(252^2-248^2)=5000#

Since this is categorized under PEMDAS, I'll answer in terms of the order of operations and assume that you have a calculator.

#1000^2/(252^2-248^2)# is a fancy way of writing #(1000^2)div(252^2-248)^2#. The P in PEMDAS stands for parentheses, and we have some parentheses, so let's work them out.

The first set of parentheses is #1000^2#. Inside those parentheses, we go through PEMDAS again. There are no further parentheses, so we can move onto E: exponents, which there is! A calculator or mental math or a table will tell you that #1000^2=1000000#. Now, we have #1000000# for our first set of parentheses and there's nothing else to do with that.

Our equation is now #1000000div(252^2-248^2)#. There are still parentheses, so we have to deal with those.

The second set of parentheses is #252^2-248^2#. Let's go through PEMDAS. There's no further parentheses, but there are exponents. #252^2=63504#, giving us #63504-248^2#. There are still exponents, so we continue. #248^2=61504#, giving us #63504-61504#. There are no more exponents, so we can move on. MD stands for multiplication and division, from left to right. Neither operation is present here, so we finally get to AS, which stands for addition and subtraction from left to right. We subtract, finding that #63504-61504=200#. So our answer for this section is #200#.

Back to the entire equation, we now have #1000000div200#. There are no more parentheses or exponents, but there is division. We find that #1000000div200=5000# Our equation is now #5000#. There is no more multiplication nor division and there is no addition nor subtraction, therefore we know that we are done!

Eli Assouline · Answer

undefined To simplify $ \frac{1000^2}{252^2 - 248^2} $, first calculate $ 252^2 - 248^2 $, which equals $ (252 + 248)(252 - 248) = 500 \times 4 = 2000 $. Then, substitute this value back into the original expression to get $ \frac{1000^2}{2000} = \frac{1000000}{2000} = 500 $. So, the simplified form is $ 500 $.