Introduction to Radicals

Adding and Subtracting Radical Expressions

Simplify the below radical expression by combining 'like' terms.

Hint: Remove all perfect square factors in each term and then add and subtract like radicals.

$2 \sqrt{32} + 5 \sqrt{18} - 3 \sqrt{8}$

Simplify the first term: $2 \sqrt{32}$

\sqrt{2} + 5 \sqrt{18} - 3 \sqrt{8}

Now simplify the second term: $5 \sqrt{18}$

8 \sqrt{2} + \sqrt{2} - 3 \sqrt{8}

Now simplify the third term: $3 \sqrt{8}$

8 \sqrt{2} + 15 \sqrt{2} - \sqrt{2}

Lastly, combine similar terms:

\sqrt{2}

Congratulations, you provided the correct answer! The simplified expression is:
$8 \sqrt{2} + 15 \sqrt{2} - 6 \sqrt{2} = 17 \sqrt{2}$