What you'll practice

Radicals add the way like terms do: $3\sqrt{2} + 2\sqrt{2} = 5\sqrt{2}$, and unlike radicals stay apart. The real skill is simplifying first — $\sqrt{8}$ hides a $2\sqrt{2}$ — so radicals that look different turn out to be like. These questions cover recognizing like radicals, simplify-then-combine, and mixed sums.

Worked example

Common mistakes

• Adding the radicands: $\sqrt{2} + \sqrt{8} \neq \sqrt{10}$. Simplify first, then combine coefficients of like radicals.
• Declaring radicals unlike without simplifying: $\sqrt{27}$ and $\sqrt{3}$ look different, but $\sqrt{27} = 3\sqrt{3}$ makes them like.
• Adding coefficients of genuinely unlike radicals: $2\sqrt{3} + 5\sqrt{2}$ cannot be combined — leave it as is.

Try a few

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FAQ

When can two radicals be added?

Only when they're like radicals — the same number under the radical after simplifying. Then add the outside coefficients and keep the radical.

Why simplify before combining?

Radicals that look unlike often aren't. √8 and √2 seem different, but √8 = 2√2 — simplifying reveals the like radical.

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

• Simplify radicals