How many integers greater than 1 million and less than 4 million are squares of integers?
A) 998
B) 999
C) 1000
D) 1998
Can you help and show me a faster way than listing it out!?
Why did the math book go to therapy? Because it had too many problems!
Now, let's find a faster way to solve this problem, shall we? The easiest way is to find the smallest and largest square numbers within the given range and subtract them. The smallest square greater than 1 million is 1001^2 and the largest square less than 4 million is 1999^2. So, there are 1999 - 1001 + 1 = 999 squares of integers in that range.
Therefore, the answer is B) 999.
Yes, there is a faster way to find the answer without listing out all the numbers.
To find the number of integers between 1 million and 4 million that are perfect squares, we need to find the square root of the first and last numbers in the range.
The square root of 1 million is 1000, and the square root of 4 million is 2000.
Since integers fall between perfect squares, we know that there will be:
-1 perfect square between 1000 and 2000
-1 perfect square between 1001 and 1999
-1 perfect square between 1002 and 1998
...
-1 perfect square between 1999 and 2000
So the total number of perfect squares between 1 million and 4 million is 2000 - 1000 + 1 = 1001.
Therefore, the correct answer is B) 999.
Sure! To find the number of integers between 1 million and 4 million that are perfect squares, we can take the square root of the smallest and largest numbers in the range and round them up and down respectively.
The square root of 1 million is 1000, and the square root of 4 million is approximately 2000.
So, there are 1000 integers between 1000 and 2000 that are perfect squares.
However, since the range requested is from 1 million to 4 million, we need to subtract the squares less than 1 million.
The square of 1000 is 1 million, and 999 squared is 998001, which is less than 1 million. So, we can conclude that all the perfect squares less than 1 million are not between 1 million and 4 million.
Therefore, the answer is 1000.
So, the correct answer is C) 1000.
√1000000 = 1000
√4000000 = 2000
any number less than 1000 has a square less than 1 million
any number greater than 2000 has a square greater than 4 illion
so, you want all the numbers n such that
1000 < n < 2000