the square of odd no.is
Answers
Step-by-step explanation:
first:
12 = 1, and that's clearly odd.
32 = 9, which is odd. We can write a table like this:
32 =
1 2 3
. .
1 1 2 3
2 4 5 6
3 7 8 9
green is for odd and purple is for even. So it continues...
52 =
1 2 3 4 5
. .
1 1 2 3 4 5
2 6 7 8 9 10
3 11 12 13 14 15
4 16 17 18 19 20
5 21 22 23 24 25
72 =
1 2 3 4 5 6 7
. .
1 1 2 3 4 5 6 7
2 8 9 10 11 12 13 14
3 15 16 17 18 19 20 21
4 22 23 24 25 26 27 28
5 29 30 31 32 33 34 35
6 36 37 38 39 40 41 42
7 43 44 45 46 47 48 49
In each row, whatever colour starts the row is the colour that ends the row. Since the diagram is a square, then there are an odd number of rows, too. That means whatever colour is at the top of a column is also at the bottom of a column. Since all the tables begin with 1, which is odd and therefore green, we can choose any arbitrary odd number and write its square table and we will get all the corners as odd.
odd2 =
1 2 ... ... ... ... odd
. .
1 odd even . even odd
2 even odd . odd even
. .
. ... ... ...
. .
. even odd . odd even
odd odd even . even odd
And you can see that this means the bottom right hand corner, which is the value of odd2 , is also going to be odd.
Stephen La Rocque.>
Hi Samantha,
If you know some algebra you can try it this way. An odd number is one more than an even number so you can write your odd number as 2n + 1 where n is an integer. Then the square of this number is
(2n + 1)(2n + 1)
Expand this to get
(2n + 1)(2n + 1) = 4n2 + 4n + 1 = 2(2n2 + 2n) + 1
which is again one more than an even number so it is odd.
Penny
hope it helps you please mark as brainliest
Answer:
Step-by-step explanation:
Let us check this by squaring odd numbers.
3²=9
7²=49
11²=121
Hence, square of an odd number is always an odd number.
Many mathematical operations have an inverse, or opposite, operation. Subtraction is the opposite of addition, division is the inverse of multiplication, and so on. Squaring, which we learned about in a previous lesson (exponents), has an inverse too, called "finding the square root." Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 …
The square root of a number, n, written
is the number that gives n when multiplied by itself. For example,
because 10 x 10 = 100
Finding square roots of of numbers that aren't perfect squares without a calculator
1. Estimate - first, get as close as you can by finding two perfect square roots your number is between.
2. Divide - divide your number by one of those square roots.
3. Average - take the average of the result of step 2 and the root.
4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.
Example: Calculate the square root of 10 () to 2 decimal places.
1. Find the two perfect square numbers it lies between.
Solution:
32 = 9 and 42 = 16, so lies between 3 and 4.
2. Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)
3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667
Repeat step 2: 10/3.1667 = 3.1579
Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623
Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001
If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.
Note: There are a number of ways to calculate square roots without a calculator. This is only one of them.
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