Numbers & Operations
Radicals
A radical (√) asks: what number multiplied by itself gives this value? Simplifying radicals means pulling out perfect square factors.
Watch & Learn
Watch a clear, friendly video explanation of Radicals:
Watch on YouTube →Opens a YouTube search for the best tutorial videos on this topic.
Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Simplify: √25
Step-by-Step Solution
25 is a perfect square.
Ask: what number times itself equals 25?
5 × 5 = 25, so √25 = 5.
Answer
5
Problem
Simplify: √81
Step-by-Step Solution
81 is a perfect square.
Ask: what number times itself equals 81?
9 × 9 = 81, so √81 = 9.
Answer
9
Problem
Add: 3√2 + 5√2
Step-by-Step Solution
Like radicals (same radicand) can be added like like terms.
3√2 + 5√2 = (3 + 5)√2 = 8√2
Answer
8√2
Problem
Simplify: √200
Step-by-Step Solution
Find the largest perfect square factor of 200.
200 = 100 × 2, and 100 is a perfect square.
√200 = √(100 × 2) = √100 × √2 = 10√2
Answer
10√2
Problem
Multiply: √3 × √12
Step-by-Step Solution
Multiply under the radical: √3 × √12 = √(3 × 12) = √36.
√36 = 6.
Answer
6
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Simplify: √36
Simplify: √50
Simplify: √72
Add: 2√3 + 7√3
Simplify: √98
Simplify: √49
Simplify: √121
Simplify: √18
Multiply: √5 × √5
Simplify: √32
Add: 4√5 + √5
Multiply: √2 × √8
Finished all 12? Give yourself a pat on the back — then check your work!
Keep going — you're on a roll!
Every topic you master is another step on your journey.
Explore More Topics