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What is a number that has integers at all its square roots?
It is a perfect square.
What are all the square roots of 1600?
Like every other number 1600 has only two square roots, plus and minus 40.
Is -10 a square root of 100?
In some sense, yes. However, due to standard mathematical notation, the square root of 100 is 10. There are some things to note. First, when we use a square root sign (or any root sign) in math, it is assumed we mean the principal root. This is the root that is greater than or equal to 0. The principal root of 100 is 10, so when asked just for the square root of 100, it is generally assumed the answer is simply 10. To be more complete, when taking all second roots of 100 (all square roots), we get 10 and -10. The number -10 is a second root of 100, just not the principal root. Finally, when considering equations such as x2 = 100, we must take the positive and negative square roots of 100 (the principal root and inverse of the principal root) to find all the solutions. We get x = 10, -10.
What kind of number system is a square root?
A square root is not a number system. Square roots of non-negative numbers may be rational or irrational, but they all belong to the set of real numbers. The square roots of negative numbers do not. To include them, the number system needs to be extended to the complex numbers.
What number is a square number but not a prime number and is less than 100?
No square number is a prime number, since it has the number you squared as a factor. There are several square numbers less than 100. Just calculate the squares of all numbers, starting with 1, until you reach or pass 100. Then stop.
