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We can continue this way to see such roots as fourth roots, fifth roots, sixth roots, and so on.
There is a symbol used to indicate roots of a number. It is called the radical sign
We discuss particular roots using the radical sign as follows:
= 7 since
since
since
In an expression such as
Find each root.
To determine the square root of 25, we ask, "What whole number squared equals 25?" From our experience with multiplication, we know this number to be 5. Thus,
Check:
To determine the fifth root of 32, we ask, "What whole number raised to the fifth power equals 32?" This number is 2.
Check:
Find the following roots using only a knowledge of multiplication.
Calculators with the , , and keys can be used to find or approximate roots.
Use the calculator to find
Display Reads | ||
Type | 121 | 121 |
Press | 11 |
Find .
Display Reads | ||
Type | 2187 | 2187 |
Press | 2187 | |
Type | 7 | 7 |
Press | .14285714 | |
Press | = | 3 |
(Which means that .)
Use a calculator to find the following roots.
For the following problems, write the expressions using exponential notation.
For the following problems, expand the terms. (Do not find the actual value.)
For the following problems, determine the value of each of the powers. Use a calculator to check each result.
For the following problems, find the roots (using your knowledge of multiplication). Use a calculator to check each result.
For the following problems, use a calculator with the keys , , and to find each of the values.
( [link] ) Use the numbers 3, 8, and 9 to illustrate the associative property of addition.
( [link] ) In the multiplication , specify the name given to the numbers 8 and 4.
8 is the multiplier; 4 is the multiplicand
( [link] ) Does the quotient exist? If so, what is it?
( [link] ) Does the quotient exist? If so, what is it?
Yes; 0
( [link] ) Use the numbers 4 and 7 to illustrate the commutative property of multiplication.
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