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True or false- every odd whole number can be written as the difference of two squares?
Wiki User
∙ 14y ago
it's true for every odd number greater than 1, because the difference between the squares of two consecutive numbers is always a unique odd number eg: 42 - 32 = 7, 52 - 42 = 9 etc etc.
Every odd number, call it x, is the sum of two consecutive numbers, call them n and
n + 1. To find the two squares that differ by x, all you need do is add n and n + 1.
Eg the squares which differ by 101 are 502 and 512 (2500 and 2601). Similarly to find the difference between the squares of two successive numbers, just add the two numbers, see examples above.
Proof: x = n + (n + 1)
(n + 1)2 - n2 = n2 + 2n + 1 - n2 = 2n + 1 = n + (n +1) = x
Wiki User
∙ 14y ago
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How many square numbers between 100 and 1000?
Infinitely many, since every positive number is a square of some other number. However, there are 21 perfect squares (SQUARES OF INTEGERS). From 112 to 312, inclusive.
The only number that is one less than a square?
Every non-negative real number is a square (every number if in the complex field) so every real number greater than or equal to -1 is one less than a square. Even if you restrict yourself to perfect squares, of the form n2, then n2 - 1 = (n-1)*(n+1) is one less than a square. There are infinitely many such numbers.
How many positive integers less than 2008 have an even number of divisors?
There are 1,963 such integers. Every factor of a number has a pair. The only time there will be an odd number of factors is if one factor is repeated, ie the number is a perfect square. So the question is really asking: how many positive integers less than 2008 (in the range 1 to 2007) are not perfect squares. √2007 = 44 and a bit (it lies between 44 and 45) So there are 44 integers less than (or equal to) 2007 which are perfect squares → 2007 - 44 = 1963 integers are not perfect squares in the range 1-2007 and have an even number of factors (divisors).
True or false- a square number is always bigger than the number?
False. It is true for every positive number greater than 1, this includes non-integers, and any number less than zero. Numbers between 0 and 1 have squares smaller than their principal square root.
What quadrilateral has two pairs of congruent sides?
Every parallelogram has. (That includes squares, rectangles, and rhombera.)
Can you express every odd prime number as the difference of two squares?
Every odd number greater than one is the difference of two squares. This includes all the odd prime numbers. To find the two numbers whose difference of squares equals a particular odd number, divide the odd number by 2. The two numbers are the integers immediately below and above that dividend. For example, 17 is the difference of two squares. Divide 17 by 2 and get 8.5. The two numbers are 8 and 9. 92 - 82 = 81 - 64 = 17.
Which ratio shows the number of black squares to every one white squares?
12:1
What is the name of the math sequence where you add every odd number?
Perfect squares.
Which numbers are NOT perfect squares?
In the complex field, every number is a square so there are no numbers that are not squares. If the domain is reduced to that of real numbers, any negative number is not a square. However, the term "square numbers" (not number's!) is often used to refer to perfect square numbers. These are numbers that are squares of integers. Therefore the squares of fractions or Irrational Numbers are non-squares.
Can every rational number be written as a quotient?
Every number can be written as a quotient.Every rational number can be written as a quotient of whole numbers.
Which numbers are not square number's?
In the complex field, every number is a square so there are no numbers that are not squares. If the domain is reduced to that of real numbers, any negative number is not a square. However, the term "square numbers" (not number's!) is often used to refer to perfect square numbers. These are numbers that are squares of integers. Therefore the squares of fractions or irrational numbers are non-squares.
Can every Whole Number be written as a decimal?
Every whole number be written as a decimal; e.g 2 can be written as 2.00
Can you express every odd prime number as the difference of two square numbers?
All odd numbers are in the form of (2n + 1) form some integer n. (2n + 1) can be expanded into (n+1)^2 + n^2, which is the difference of two squares.
How many square numbers between 100 and 1000?
Infinitely many, since every positive number is a square of some other number. However, there are 21 perfect squares (SQUARES OF INTEGERS). From 112 to 312, inclusive.
What shapes have perallel opposite sides?
-- every parallelogram (including rectangles, squares, and rhombera)-- trapezia (trapezoids)-- every regular polygon with an even number of sides
What is an example of a non perfect square?
Well, the basic idea is that every positive number is the square of some number. For example, 2 is the square of a number known as the square root of 2; 3 is the square of a number known as the square root of 3; etc. The "perfect squares" are the squares of integers. That would make all other numbers "non-perfect squares", though this term is not usually used in practice.
What is the definition of a common difference in a sequence?
common difference is the difference in every two consecutive numbers in the sequence .. or in the other way around, its the number added to a number that resulted to the next number of the sequence ..
