Is the statement below correct for all numbers?
The square of a number is greater than the number itself.
explain how you know
2007-07-05 06:27:22 · 21 answers · asked by Top_Gear_Biggest_Fan 5 in Science & Mathematics ➔ Mathematics
nope. for example 0.5 squared is 0.25 which is smaller.
hmm someone got there first.
2007-07-05 06:30:52 · answer #1 · answered by Anonymous · 3⤊ 1⤋
For example: The square route of 16, 4? 4 is obviously less than 16. So the square route of a number will always be lesser unless that number is 1 or below. So the statement is wrong.
2007-07-05 13:37:47 · answer #2 · answered by Anonymous · 0⤊ 1⤋
No. For 0 and 1, the square is equal to the number, since 0^2 = 0 and 1^2 = 1. For numbers greater than 0 and smaller than 1, the square is smaller than the number. For example, 0.5^2 = 0.25, 0.3^2 = 0.09, and 0.15^2 = 0.0225. Only for numbers less than 0 or greater than 1 is the square larger than the number itself.
2007-07-05 13:30:26 · answer #3 · answered by DavidK93 7 · 4⤊ 0⤋
It is untrue for all numbers. It is true for all numbers except those lying in between 0 and 1.
Like 0.5*2 is 0.25 smaller
Also (-0.5)*2 is 0.25 which is greater. Many above have made this mistake :)
So if a number lies between 0 and 1 ,both inclusive, its square will not be greater than the number itself.
2007-07-05 16:11:40 · answer #4 · answered by Y L 2 · 0⤊ 0⤋
All whole numbers and intergers this is correct.
If you sqare a negative number the answer is positive so that would even be correct for negative numbers.
However the statment is incorrect because of fractions and decimals.
1/4 ^2 = 1/16 which is smaller than 1/4
2007-07-05 13:40:28 · answer #5 · answered by quickgun 3 · 0⤊ 0⤋
Only for numbers greater than 1
2007-07-05 13:30:29 · answer #6 · answered by Kyle G 4 · 3⤊ 1⤋
It is NOT always true.
The square of a positive number over one will always be greater than itself.
The square of a negative number less than -1 will always be greater than itself because two negatives multiplied make a positive number.
But the square of a positive number less than one (ie 1/2) will be smaller - and half times a half is a quarter.
I studied maths at A-level - but many years ago now and couldn't explain the reasons although we did learn them.
2007-07-05 13:33:07 · answer #7 · answered by keys780 5 · 0⤊ 1⤋
No it is not true for the square of 1 which is 1.
For all other whole numbers it must be true. How do I know? Simple logic. If you multiply a whole number by itself the result (with the exception of 1) must be bigger than itself.
For fractions the result would be less than the original number before it is squared.
2007-07-05 13:39:13 · answer #8 · answered by BARROWMAN 6 · 0⤊ 1⤋
This is true if the number is greater than 1or less than 0.
But 1^2=1 which is not greater than 1
and .8^2=.64<.8
You can see this by graphing y=x^2 and y=x on the same axis.
y=x is above y=x^2 on the interval (0,1)
2007-07-05 13:33:57 · answer #9 · answered by Anonymous · 0⤊ 1⤋
No. If the number x is
0 <= x < 1
Then it's square will be less than the number.
Example
(1/2)^2 = 1/4 (i.e. 0.25 < 0.5)
2007-07-05 13:36:50 · answer #10 · answered by Tom S 7 · 0⤊ 1⤋
No, it is not correct.
It is only correct for numbers between 0 and one. For numbers less than or equal to one, the square of those numbers will be less than or equal to the number itself.
For numbers less than zero, the square will be greater than the number itself, because the square of a negative number is positive.
2007-07-05 13:31:07 · answer #11 · answered by Brian L 7 · 3⤊ 1⤋