In general:
If a and b are positive numbers, then
Note:
Simplest Form of a Surd
A surd is said to be in its simplest form if the number under
the root sign has no perfect square as a factor.
In general:
To simplify a surd, write the number under the root sign as the product
of two factors, one of which is the largest perfect square.
Note that the factor 16 is the largest perfect square.
Recall that the numbers 1, 4, 9, 16, 25, 36, 49, … are perfect
squares.
Example 4
Solution:
The square numbers are 1, 4, 9, 16, 25, 36, 49, .... By trying
each one in turn, we find that the largest perfect square that is a factor
of 48 is 16.
Example 5
Solution:
Look for perfect squares that are factors of 63. Try 4, 9, 16 etc.
Alternative Method
Example 6
Solution:
Look for perfect squares that are factors of 12. Try 4, 9, 16
etc.
Example 7
Key Terms
entire surd, mixed surd, simplest
form, perfect squares |
