Square root problems


In this lesson, you'll learn how to solve square root problems. Remember √ is the symbol for square root.


So what is the square root of a number n (√n)?


It's that figure which squared (i.e. multiplied by itself) gives n.


If n is a square number (perfect square) (1, 4, 9, 16, 25, 36, 49, 64, 81, 100 etc), its square root is a whole number.


However, if n is a non-square number (2, 3, 5, 6, 7, 8, 10, 11, 12, 13 etc), its square root is a decimal and your calculator will prove useful!


Let's take a look at the square roots of square numbers first.


How to find square root of 1


What figure squared (times by itself) gives 1?


The answer is 1 because

1²   =   1  x  1   =   1


Therefore



Square root of 4


Which figure squared (multiplied by itself) gives 4?


The answer's 2

2²   =   2  x  2   =   4


So



Square root of 9


What figure squared (times by itself) gives 9?


The answer's 3

3²   =   3  x  3   =   9


So



Now try finding the square roots of the remaining square numbers up to 100


Here are the workings out!


  • 16 = 4  (4² = 4 x 4 = 16)
  • 25 = 5  (5² = 5 x 5 = 25)
  • 36 = 6  (6² = 6 x 6 = 36)
  • 49 = 7  (7² = 7 x 7 = 49)
  • 64 = 8  (8² = 8 x 8 = 64)
  • 81 = 9  (9² = 9 x 9 = 81)
  • 100 = 10  (10² = 10 x 10 = 100)


See how these square roots are whole numbers?


Next how about the square roots of non-square numbers?


Reach for your calculator, enter 2 followed by the square root (√) button



The display should show

1.414213562


You've just worked out √2 - the square root of 2.


Notice how it's a decimal and this applies to the square roots of other non-square numbers - for instance, check the following on your calculator


  • √3   =   1.732050808
  • √5   =   2.236067978
  • √6   =   2.449489743
  • √7   =   2.645751311
  • √8   =   2.828427125
  • √10   =   3.16227766
  • √11   =   3.31662479
  • √12   =   3.464101615
  • √13   =   3.605551275


Happy you can now handle square root problems?


As you can see, finding the square root of a number n may or may not require use of your calculator depending on whether n is a square number (square root = whole number) or a non-square number (square root = decimal).


For related topics click:

Square numbers

Cube numbers

Cube roots


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