Adding and Subtracting Radical Expressions – Practice Problems

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To add or subtract radical expressions, first simplify radicals and then combine like radical terms.

Only like radical terms, or radical expressions which share the same index and radicand, can be added or subtracted. For example, 3√5 + 4√5 = 7√5. In the same manner, 8√3 - 6√3 = 2√3. What about if we’re given with √12 - √48? This becomes √4(3) - √(16)(3) = 2√3 - 4√3 = -2√3.

Radical expressions with different radicands or indices can’t be added or subtracted. Simplifying 9√5 - 2√2 - 3√5 + 5√2 gives us (9√5 - 3√5) + (- 2√2 + 5√2) = 6√5 + 3√2.

Simplifying radical expressions by adding or subtracting radicals is as easy as adding or subtracting like terms in an algebraic expression.

Rewrite expressions involving radicals and rational exponents using the properties of exponents.


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Exercises in this Practice Problem
Explain how to add and subtract radical expressions.
Simplify the following expression.
Decide which terms can be added or subtacted.
Find the errors in the calculation.
Determine when radical expressions can be added or subtracted.
Add or subtract the following radical expressions.