This lesson from OpenStax Elementary Algebra 2E teaches students how to add and subtract like square roots by combining coefficients when radicands match, just as they would combine like terms in algebra. Students also learn to simplify square roots using the Product and Quotient Properties before adding or subtracting expressions with unlike radicands. Real-world applications, such as finding garden dimensions and calculating falling-object times, reinforce these radical arithmetic skills.
Section 1
📘 Add and Subtract Square Roots
Master adding and subtracting square roots by treating them like algebraic terms. You'll combine like square roots—those with the same radicand—and simplify others, like , to find hidden like terms before performing the operation.
Get ready to apply this concept! Next up are interactive examples and practice cards that break down simplifying and combining radicals step-by-step.
Section 2
Like Square Roots
Square roots with the same radicand are called like square roots.
We add and subtract like square roots in the same way we add and subtract like terms.
Trying to add square roots with different radicands is like trying to add unlike terms.
Section 3
Add and Subtract Like Square Roots
To add or subtract like square roots, add or subtract their coefficients.
The radicand remains the same.
This process is similar to combining like terms in algebra, such as .
Similarly, .
Section 4
Simplify before combining
Sometimes when we have to add or subtract square roots that do not appear to have like radicals, we find like radicals after simplifying the square roots.
Always simplify square roots by removing the largest perfect-square factor.
Section 5
Combining roots with variables
When radicals contain variables, they are considered like radicals if the radicand (both the constant and variable parts) is identical after simplification.
First, simplify each radical by removing all perfect-square factors, then combine the coefficients of any like radicals.
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Section 1
📘 Add and Subtract Square Roots
Master adding and subtracting square roots by treating them like algebraic terms. You'll combine like square roots—those with the same radicand—and simplify others, like , to find hidden like terms before performing the operation.
Get ready to apply this concept! Next up are interactive examples and practice cards that break down simplifying and combining radicals step-by-step.
Section 2
Like Square Roots
Square roots with the same radicand are called like square roots.
We add and subtract like square roots in the same way we add and subtract like terms.
Trying to add square roots with different radicands is like trying to add unlike terms.
Section 3
Add and Subtract Like Square Roots
To add or subtract like square roots, add or subtract their coefficients.
The radicand remains the same.
This process is similar to combining like terms in algebra, such as .
Similarly, .
Section 4
Simplify before combining
Sometimes when we have to add or subtract square roots that do not appear to have like radicals, we find like radicals after simplifying the square roots.
Always simplify square roots by removing the largest perfect-square factor.
Section 5
Combining roots with variables
When radicals contain variables, they are considered like radicals if the radicand (both the constant and variable parts) is identical after simplification.
First, simplify each radical by removing all perfect-square factors, then combine the coefficients of any like radicals.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter