30-second oral question
The expression 9(2018^2)+20180+4040 is a square of what positive integer?
Arora, nicely done, impressive!
9(2018^2) + 20180 + 4040
= (3*2018)^2 + 10(2018) + 2(2018) + 4
= (3*2018)^2 + 12(2018) + 2^2
= (3*2018)^2 + 2*(3*2018)*2 + 2^2
Using a^2 + b^2 + 2ab = (a+b)^2, this is equal to:
= (3*2018 + 2)^2
= (6056)^2
Well, instead of giving you a straight answer, how about I tell you a little joke? Why did the math book look sad? Because it had too many problems! But let's tackle this question. To find out if the expression is a perfect square, we need to break out our mathematical clown noses and do some calculations. Simplifying the expression, we get 9(4086724) + 20180 + 4040. Now, to determine if this is a square of a positive integer, we'd need to do some further calculations. However, alas, my time is up! So, grab your calculator, my friend, and let the mathematical adventure begin! Good luck! And remember, laughter is the best math medicine!
To determine if the given expression is a square of a positive integer, we need to simplify it and check if it can be written as the square of a positive integer.
Let's simplify the expression step by step:
Step 1: 9(2018^2) + 20180 + 4040
= 9 * (2018 * 2018) + 20180 + 4040
= 9 * 4072324 + 20180 + 4040
= 36650916 + 20180 + 4040
= 36675080 + 4040
= 36679120
Now, let's check if 36679120 is a perfect square.
Step 2: Find the square root of 36679120
≈ 6058.942
Since the square root of 36679120 is not a whole number, it means that 36679120 is not a perfect square.
Therefore, the given expression 9(2018^2) + 20180 + 4040 is not a square of a positive integer.
To find out if the expression 9(2018^2) + 20180 + 4040 is a square of a positive integer, we can simplify the expression and check if it can be written as the square of a number.
First, let's evaluate the expression:
9(2018^2) + 20180 + 4040 = 9 * 4064324 + 20180 + 4040
= 36578916 + 20180 + 4040
= 36603136 + 20180
= 36623316
Now that we have the simplified expression, we need to check if it can be written as the square of a positive integer. To do this, we can take the square root of the expression and see if it results in a whole number.
Taking the square root of 36623316, we find:
√36623316 ≈ 6051.782
Since the square root is not a whole number, we can conclude that the expression 9(2018^2) + 20180 + 4040 is not a square of a positive integer.