Adding and Subtracting Radicals

Adding and Subtracting Radicals

How to add and subtract radicals: examples and their solutions.

Example 1

Simplify the given expression. 3sqrt(2) + 2sqrt(5) + 5sqrt(2) - 8sqrt(5)

Just like the like terms in a polynomial,
only like radicals
(terms that have the same radical)
can be added or subtracted.

3√2 and +5√2 are like terms.
So 3√2 + 5√2 = (3 + 5)√2.

2√5 and -8√5 are like terms.
So 2√5 - 8√5 = (2 - 8)√5.

Example 2

Simplify the given expression. sqrt(50) + sqrt(18) - sqrt(2)

To add and subtract these radicals,
simplify50 and √18.

5√2, +3√2, and √2 are all like radicals.

So you can now add and subtract them.