## Simplifying radicals: Section 2Simplifying the square roots of powers Simplifying the square roots of powers
Example 4. Since the ( -- then the square root of an even power will be = As for an odd power, such as
Therefore, = = (These results hold only for
Problem 5. Simplify each radical. (Assume To see the answer, pass your mouse over the colored area.
Problem 6. Simplify each radical. Remove the
Problem 7. True or false? That is, which of these is a rule of algebra? (Assume that
Problem 8. Express each radical in simplest form. a) = = 2.
To simplify a radical, the radicand must be composed of b) =
= 2 c) =
= 3 Fractional radicand A radical is in its simplest form when the radicand is not a fraction. Example 5. The denominator a square number. When the denominator is a square number, as , then
In general, For,
Problem 9. Simplify each radical.
Example 7. The denominator not a square number. Simplify .
Example 8. Simplify . (Assume that the variables do not have negative values.)
Problem 10. Simplify each radical. (Assume that the variables do not have negative values.)
A problem that asks you to show, means to write what's on the left, and then transform it algebraically so that it looks like what's on the right.
We can identify with the absolute value of . For when . But if
because the square root is never negative. (Lesson 26.) Rather, when . . Therefore in general we must write . conforms to the definition of the absolute value. Next Lesson: Multipying and dividing radicals Please make a donation to keep TheMathPage online. Copyright © 2021 Lawrence Spector Questions or comments? E-mail: [email protected] |