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To square a number multiply it by itself (or use a calculator's square button).
For square roots they can be worked out:
1) using a calculator's square root button;
2) take the log of the number (using a calculator or tables), divide it by two and then find the antilog (to the same base, using a calculator or tables) of this result;
3) a kind of long "division":
3.1) write the number in pairs of digits starting either side of the decimal point; if there is an odd number of digits before the decimal point, the first "pair" will be a single digit; if there is an odd number of digits after the decimal point, add a zero to make the last "pair" two digits, eg 123.456 becomes 1 23 . 45 60;
3.2) write in a "bus stop" division over the number (to make it the "dividend"), but extend the down-stroke down a few lines and put a decimal point in the answer over the decimal point in the number;
3.3) find the smallest number that when squared is not greater than the first pair of digits
3.4) write this number to the left of the down-stroke (as the divisor in a division) and over the first pair of digits
3.5) write the square of this number under the first pair of digits and subtract
3.6) bring down the next pair of digits from the "dividend"
3.7) double the answer so far (ignore the decimal point) and write to the left of the down-stroke next to the number formed in step 3.6, leaving room to add a units digit
3.8) find the digit than when added as the units digit to the "divisor" just written (in step 3.7) and the whole "divisor" is multiplied by this digit is not greater than the number formed in step 3.6;
3.9) write this digit as the units digit and over the pair of digits brought down
3.10) multiply the whole divisor by this digit (its units digit) and subtract from the number formed in step 3.6;
3.11) repeat from step 3.6 until there are no more pairs to bring down and the result of the last subtraction is 0, or until the required accuracy is found.
eg √2:
_______1_._4__1__4_2
______-------------------
____1_| 2 . 00 00 00 00
______| 1
______|---
___24_| 1__00
______| ___96
______|--------
__281_|_____4 00
______|_____2 81
______|_____------
_2824_|_____1 19 00
______|_____1 12 96
______|_____----------
28282_|_______6 04 00
______|_______5 65 64
______|_______---------
______|________ 38 36
etc
→ √2 ≈ 1.414
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What two whole numbers are between the square root of 60?
The square root of 60 is a single number; you can't have other numbers "between" it. It does work the other way, though - the square root of 60 is between other numbers.
What is the square root of 64 and how did you work it out?
The square root of 64 is 8 and you can work it out using the square root algorithm.
How do you work out the square root of 10?
There is no formula. You have to try multiplying all the numbers until you get 10.
Is the square root of four hundred and forty one twenty two?
Yes it is. Do you want to know something spectacular? Well, it's not too great. But if you switch 21 around to make 12, 12 is the square root of 144, which has the same numbers as 441! Isn't that cool. So if you know what 12 is the square root of, you know what 21 is the square root of. WARNING: THIS DOES NOT WORK WITH ALL NUMBERS!!!!!!!!!!!!
How do you evaluate a square root?
You know to find out which out which number has been timed by itself to make the number in the square root. For example: If the number inside the square root is 49, you need to find out which number has been timed by itself to make 49. As you may know, the number inside the square root is always a square number, so I would advise you to learn the list of square numbers. 7 x 7= 49, so the square root of 49 is 7. Remember that Evaluate simply means work out. So when to asked to evaluate a square number, cube number, square root, cube root etc., simply just work it out. Evaluating powers and roots is grade D in maths.
What two whole numbers are between the square root of 60?
The square root of 60 is a single number; you can't have other numbers "between" it. It does work the other way, though - the square root of 60 is between other numbers.
How do I work out the saquare root of a number?
Finding the square root of a number is the inverse operation of squaring that number. Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers. The square root of a number, n, written below is the number that gives n when multiplied by itself.
How do you work out surds?
Surds are normally irrational numbers but they can be simplified for instance the square root of 12 can be expressed as 2 times the square root of 3
What is the square root of 64 and how did you work it out?
The square root of 64 is 8 and you can work it out using the square root algorithm.
How do you work out the square root of 10?
There is no formula. You have to try multiplying all the numbers until you get 10.
What did rms stand for?
RMS is root mean square in physics. RMS is Railway Mail Sevice in postal net work rms ie root mean square is got first squaring the positive and negative values to make them all positive. Then mean is taken. After that we have to take square root of the mean square. So square Root of the Mean value of the Squares of the values. Hence the name
How do you work out square root of 81?
Find the numbers which, when multiplied by themselves, give the answer 81. The answers are -9 and +9.
Is the square root of four hundred and forty one twenty two?
Yes it is. Do you want to know something spectacular? Well, it's not too great. But if you switch 21 around to make 12, 12 is the square root of 144, which has the same numbers as 441! Isn't that cool. So if you know what 12 is the square root of, you know what 21 is the square root of. WARNING: THIS DOES NOT WORK WITH ALL NUMBERS!!!!!!!!!!!!
Find three numbers such that the sum of the squares of the smaller two are equal to the square of the third?
The numbers 3, 4, and 5 work: 32 + 42 = 52 9 + 16 = 25
What is the Square root of an isosceles triangle?
It is actually impossible to work out the square root of a shape but you can work out the square roots of the interior and exterior angles, the area and the perimiter
Who were the mathematician who worked on squares and square roots?
The first people to work on squares were probably the Sumerians (ca 2500 BCE). They made multiplication tables, so they would have known squares, like 5x5=25.The Greeks thought that any number could be expressed as a ratio of two natural numbers, as in 0.6 = 3/5. However someone realized, and then proved that the ratio of the diagonal of a square to the side can't be as a ratio - it's an irrational number, the square root of 2.Historians don't know for sure who thought of this, but it may have been Pythagoras, or someone in his school.
When you subtract one square number from another square number the answer is 3 what are the two numbers?
The numbers are 1 and 4 (the squares of 1 and 2) because 22 - 12 = (4 - 1) = 3For the difference of consecutive positive squares, the formula is (n+1)2 - n2 = 2n +1the only integer n that yields 3 is 1.*For non-integers, any square roots of numbers 3 apart will also work.
