1. The Calculator -- Most every calculator will have a square root key, the one with a radical sign () imprinted on it.  To find the square root of a number, all you have to do is enter your number, and the press the square root key.  Usually, a calculator will carry the square root out to seven or more places past the decimal point (if it is an irrational square root).
    
   For cube roots -- and other powers higher that square roots -- you will need a scientific calculator.
   
   
2. Math Tables -- To find square roots, you can use math tables, such as Table 1. As you can see, Table 1 carries the roots out to three places past the decimal point, which will usually serve your needs in finding square roots.  Table 1 provides squares and square roots of numbers from one to 150.  The square roots of numbers in Table 1 are under the 'radical sign' column.
   Let's use Table 1 to find the square root of 11, and carry our answer out to two decimal places.  If you look under the No. Column '11,' and then look under the radical sign, you can see that the square root of 11 is 3.317.  Since we are carrying our answer out to two places, we raised the value of the '1' in the hundredths position.  When dropping digits from an answer in math, it is common practice to increase the last digit you are keeping by one if the first one you're dropping is 5 or above or to leave it as is if the first one you're dropping is 4 or below.  Let's apply this principle, and use Table 1 to find some other square roots to two places:
   
   
   • The square root of 21 is 4.58
   • The square root of 29 is 5.39
   • The square root of 109 is 10.44
   • The square root of 127 is 11.27
   • The square root of 150 is 12.25
     
     
3. Pencil and Paper Computation -- You can always find the square root of a number by pencil and paper computation -- if you learn and memorize the method for computing square roots.  You can learn to use this method by completing the supplement to this lesson.  The steps involved in square root computation are shown in detail, and you can learn how to do it if you choose to.  Most often, however, calculators or square root tables are used for this purpose.

Most often, math students will use calculators or math tables to find the roots of numbers. And even though you can use any calculator to find square roots, you will need a scientific calculator to find cube roots or other higher powered roots.

Table 1: Squares & Square Roots

Summary (top)

In this lesson we have we have seen that exponents are used to show that numbers are 'raised' to powers by multiplying a number by itself as indicated by exponents.  We have 'squared' numbers, cubed numbers and raised numbers to fourth and fifth powers, etc.

We have also found the 'roots' of numbers; such as square roots, cube roots, etc., and learned that roots of numbers are indicated when they are placed under the radical sign.

We have shown that when we calculate roots of numbers, we sometimes get rational roots, and sometimes irrational roots.  Rational roots are those that result when one integer is divided by another, while irrational roots will have continuing remainders that never represent an exact value.  We also showed the difference between real and imaginary numbers.  Real numbers are those that name a specific quantity, while imaginary numbers cannot exist by using any of the math we have learned.

Finally, we showed how to find roots of numbers by using a calculator and by using mathematical tables.

By raising numbers to powers, and calculating roots as demonstrated in this lesson, you will be able to solve many problems that are encountered in algebra and geometry.

Play Square Root Flashcards by going to the website below:
www.aplusmath.com/Flashcards/sqrt.html.