Math and Arithmetic

Numbers

# How many Positive integers less than 1000 are multiples of 11 whose square roots are whole numbers?

Top Answer

###### Wiki User

###### June 28, 2017 8:56PM

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)

## Related Questions

###### Asked in Math and Arithmetic, Algebra

### What is closed under subtraction?

The set of all integers;
the set of all rational numbers;
the set of all real numbers;
the set of all complex numbers.
Also their multiples - for example
the set of all multiples of 2;
the set of all multiples of 2.5;
the set of all multiples of sqrt(17);
the set of all multiples of 3 + 4i where i is the imaginary
square root of -1.

###### Asked in Math and Arithmetic, Algebra, Geometry, Prime Numbers, Numbers

### What is the number of non-square numbers between 2 consecutive numbers?

There is no such thing as consecutive numbers because numbers
are infinitely dense. Between any two numbers there is another and
so there is no such thing as a "next" number.
There are no integers (square or non-square) between any two
consecutive integers. There are infinitely many numbers between any
two consecutive integers and, if the integers are non-negative,
every one of these will be a square of some number so the answer is
none. If the integers are negative then the
infinitely many numbers will have a square root in the complex
field but not in real numbers. In this case the answer is either
none or infinitely many, depending on the domain.

###### Asked in Math and Arithmetic

### What are the square numbers from 576 to 10000?

The square numbers integers between 576 and 10000 (and their
square roots, in the left column) are:
245762562526676277292878429841309003196132102433108934115635122536129637136938144439152140160041168142176443184944193645202546211647220948230449240150250051260152270453280954291655302556313657324958336459348160360061372162384463396964409665422566435667448968462469476170490071504172518473532974547675562576577677592978608479624180640081656182672483688984705685722586739687756988774489792190810091828192846493864994883695902596921697940998960499980110010000

###### Asked in Math and Arithmetic, Numbers

### What is the produkt of negative integer with itself?

A product of two integers is those two numbers multiplied
together. If the product is two integers, it is called a square.
Two negative integers are multiplied together by multiplying them
together just as if they are positive. For example, -3x-3=9. It is
exactly the same thing as squaring a positive integer.