Examples of such numbers are 49, where sqrt(49) = 7, 81, where sqrt(81) = 9.
Such numbers are called square numbers.
Correct.
its called a "perfect square"
A perfect square.
A perfect square.
What are the integers between 0 and 100 whose positive square roots are integers?
To have a whole number square root, the number is a perfect square. Thus the numbers will be the squares of multiples of 11. Thus the first number will be (1×11) × (1×11) = 11² = 121 The next candidate will be (2×11) × (2×11) = 22² = 484 The next possible candidate will be (3×11) × (3×11) = 33² = 1089 which is too large. Thus there are two multiples of 11 less than 1000 whose square roots are whole numbers, namely 121 (11²) and 484 (22²)
its called a "perfect square"
A perfect square.
A perfect square.
A perfect square.
A perfect square is a number whose square root is a whole number, such as 1, 4, 9, 16, 25, etc.
If the square root is a whole number, then the square of the square root, the original number, is also a whole number; all whole numbers can be expressed as themselves over 1, and so are rational numbers. The answer is thus any square number, ie the square of the natural numbers: 1 (1²), 4 (2²), 9 (3²), 16 (4²), etc.
For the same reason that the square root of ANY negative number is not a real number.Real numbers are positive, negative, or zero. * The square of a positive number is a positive number. * The square of a negative number is a positive number. * The square of zero is zero. In other words, in no case will you get a REAL number whose square is a negative number. The square roots of negative numbers are said to be "imaginary" - a name given for historical reasons. They are just as "real" or "unreal" as the so-called real numbers, but the point is that they are a different kind of numbers.
* Its square root is a whole #. Example: 16 is a perfect square. Its square root is 4. 17 is not a perfect square. Its square root is around 4.123105626
What are the integers between 0 and 100 whose positive square roots are integers?
You get another number whose magnitude will be greater than the original number. Whether it is bigger or smaller will depend on whether the whole number was positive or negative.
To have a whole number square root, the number is a perfect square. Thus the numbers will be the squares of multiples of 11. Thus the first number will be (1×11) × (1×11) = 11² = 121 The next candidate will be (2×11) × (2×11) = 22² = 484 The next possible candidate will be (3×11) × (3×11) = 33² = 1089 which is too large. Thus there are two multiples of 11 less than 1000 whose square roots are whole numbers, namely 121 (11²) and 484 (22²)
3 and 84.