Adding, Subtracting, and Dividing Radical Expressions

1
Adding, Subtracting, and Dividing Radical
Expressions
10.4
2
Combining Radicals
EXAMPLE
Simplify (add or subtract) by combining like
radical terms
SOLUTION
Apply the distributive property.
Simplify.
Group like terms.
Apply the distributive property.
Simplify.
3
Combining Radicals
EXAMPLE
Simplify by combining like radical terms, if
possible
SOLUTION
Factor the radicands using the greatest perfect
square factors.
Take the square root of each factor.
Apply the distributive property.
4
Combining Radicals
CONTINUED
Simplify.
Factor the radicands using the greatest perfect
cube factors.
Take the cube root of each factor.
Apply the distributive property.
Simplify.
5
Simplifying Radicals
6
Simplifying Radicals
EXAMPLE
Simplify using the quotient rule
SOLUTION
7
Combining Radicals
8
Combining Radicals
EXAMPLE
Divide and, if possible, simplify
SOLUTION
In each part of this problem, the indices in the
numerator and the denominator are the same.
Perform each division by dividing the radicands
and retaining the common index.
Divide the radicands and retain the common index.
Divide factors in the radicand. Subtract
exponents on common bases.
9
Combining Radicals
CONTINUED
Simplify.
Factor using the greatest perfect square factor.
Factor into two radicals.
Simplify.
Divide the radicands and retain the common index.
Divide factors in the radicand. Subtract
exponents on common bases.
10
Combining Radicals
CONTINUED
Simplify.
Factor using the greatest perfect square factor.
Factor into two radicals.
Simplify.