How do you simplify a square root?

Factor out the largest perfect square, take its root outside the radical, and leave the rest inside. √72 = √(36·2) = 6√2.

How do you know when a radical is fully simplified?

When the number under the radical has no perfect-square factor left other than 1. If you can still divide it by 4, 9, 16, 25… evenly, keep going.

Yes — this skill is one of the free ones. Every unit opens with free skills, no account needed. Premium ($6/month or $30/year) unlocks every skill plus the parent progress dashboard.

How is this different from IXL?

No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is reviewed by a human before you see it.

Algebra 2 practice

Simplifying Radicals — Practice

Rewrite radicals like $\sqrt{72}$ in simplest form — free, no account, with the reasoning shown on every question.

Start practicing — free

No login, no card. Open Algebra 2 and pick the tile.

What you'll practice

Simplifying a radical means factoring out the largest perfect square: $\sqrt{72} = \sqrt{36 \cdot 2} = 6\sqrt{2}$ . It's the skill that keeps every later radical operation manageable. These questions cover finding the largest perfect-square factor, common near-misses, and recognizing when a radical is already simplest.

Worked example

Simplify $\sqrt{72}$ .

Find the largest perfect square dividing $72$ : check $36$ — $72 = 36 \times 2$ . ✓
Split the radical: $\sqrt{72} = \sqrt{36} \cdot \sqrt{2}$ .
Evaluate the perfect square: $\sqrt{36} = 6$ .
$\sqrt{72} = 6\sqrt{2}$ . (Using a smaller square like $4$ works too, but takes more rounds: $\sqrt{72} = 2\sqrt{18} = 2 \cdot 3\sqrt{2} = 6\sqrt{2}$ .)

Common mistakes

Stopping at a smaller perfect square: $\sqrt{72} = 2\sqrt{18}$ isn't finished — $18$ still contains the perfect square $9$ .
Splitting over addition: $\sqrt{9 + 16} \neq 3 + 4$ . The radical splits over multiplication only.
Multiplying the outside number into the radical when checking: $6\sqrt{2}$ means $6 \times \sqrt{2}$ , and squaring gives $36 \times 2 = 72$ .

Try a few

1. Simplify $\sqrt{50}$ .

$5\sqrt{2}$
$2\sqrt{5}$
$25\sqrt{2}$
$5\sqrt{10}$

2. Simplify $\sqrt{48}$ .

$4\sqrt{3}$
$2\sqrt{12}$
$3\sqrt{4}$
$16\sqrt{3}$

3. Simplify $\sqrt{125}$ .

$5\sqrt{5}$
$25\sqrt{5}$
$5\sqrt{25}$
$\sqrt{125}$ is already simplest

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FAQ

How do you simplify a square root?: Factor out the largest perfect square, take its root outside the radical, and leave the rest inside. √72 = √(36·2) = 6√2.
How do you know when a radical is fully simplified?: When the number under the radical has no perfect-square factor left other than 1. If you can still divide it by 4, 9, 16, 25… evenly, keep going.
Is Cramzoo free?: Yes — this skill is one of the free ones. Every unit opens with free skills, no account needed. Premium ($6/month or $30/year) unlocks every skill plus the parent progress dashboard.
How is this different from IXL?: No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is reviewed by a human before you see it.

Related Algebra 2 skills

Add and subtract radicals

Ready to practice?

Every question reviewed. Mistakes turn into explanations, never a score that punishes you for trying.

Start practicing — free

No login, no card. Open Algebra 2 and pick the tile.