First learn about Squares, then Square Roots are easy. Show
How to Square A NumberTo square a number: multiply it by itself. Example: What is 3 squared?
"Squared" is often written as a little 2 like this:
Squares From 02 to 62
Negative NumbersWe can also square negative numbers. That was interesting! When we square a negative number we get a positive result. Just the same as squaring a positive number: (For more detail read Squares and Square Roots in Algebra) Square RootsA square root goes the other way: 3 squared is 9, so a square root of 9 is 3 A square root of a number is ... ... a value that can be multiplied by itself to give the original number. A square root of 9 is ... ... 3, because when 3 is multiplied by itself we get 9. It is like asking: What can we multiply by itself to get this?
Here are some more squares and square roots:
Decimal NumbersIt also works for decimal numbers. Try the sliders below (note: '...' means the decimals continue on forever): Using the sliders:
NegativesWe discovered earlier that we can square negative numbers: Example: (−3) squared(−3) × (−3) = 9 And of course 3 × 3 = 9 also. So the square root of 9 could be −3 or +3 Example: What are the square roots of 25?(−5) × (−5) = 25 5 × 5 = 25 So the square roots of 25 are −5 and +5 The Square Root Symbol
We use it like this: and we say "square root of 9 equals 3" Example: What is √25?25 = 5 × 5, in other words when we multiply 5 by itself (5 × 5) we get 25 So the answer is: √25 = 5 But wait a minute! Can't the square root also be −5? Because (−5) × (−5) = 25 too.
Example: What is √36 ?Answer: 6 × 6 = 36, so √36 = 6 Perfect SquaresThe Perfect Squares (also called "Square Numbers") are the squares of the integers:
Try to remember them up to 12. Calculating Square RootsIt is easy to work out the square root of a perfect square, but it is really hard to work out other square roots. Example: what is √10?Well, 3 × 3 = 9 and 4 × 4 = 16, so we can guess the answer is between 3 and 4.
Getting closer to 10, but it will take a long time to get a good answer! At this point, I get out my calculator and it says: 3.1622776601683793319988935444327 But the digits just go on and on, without any pattern. So even the calculator's answer is only an approximation ! Note: numbers like that are called Irrational Numbers, if you want to know more. The Easiest Way to Calculate a Square Root
And also use your common sense to make sure you have the right answer. A Fun Way to Calculate a Square RootThere is a fun method for calculating a square root that gets more and more accurate each time around:
And so, after 3 times around the answer is 3.1623, which is pretty good, because: 3.1623 x 3.1623 = 10.00014 Now ... why don't you try calculating the square root of 2 this way? How to GuessWhat if we have to guess the square root for a difficult number such as "82,163" ... ? In that case we could think "82,163" has 5 digits, so the square root might have 3 digits (100x100=10,000), and the square root of 8 (the first digit) is about 3 (3x3=9), so 300 is a good start. Square Root DayThe 4th of April 2016 is a Square Root Day, because the date looks like 4/4/16 The next after that is the 5th of May 2025 (5/5/25) 309,310,315, 1082, 1083, 2040, 3156, 2041, 2042, 3154 |