50+ Radical Expressions worksheets on Quizizz | Free & Printable - Free Printable

Let’s solve each problem step by step.

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1. Simplify:
$\sqrt{2x^2 y^3}$

Break it into parts:
- $\sqrt{2}$
- $\sqrt{x^2} = |x|$, but since this is algebra (no domain specified), assume $x \ge 0$, so $\sqrt{x^2} = x$
- $\sqrt{y^3} = \sqrt{y^2 \cdot y} = y\sqrt{y}$

So:
$$
\sqrt{2x^2 y^3} = \sqrt{2} \cdot x \cdot y \sqrt{y} = xy \sqrt{2y}
$$

✔ Option C: $xy\sqrt{2y}$

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2. Simplify:
$\sqrt{128 a^3 b^4}$

Factor 128:
$128 = 64 \cdot 2 = 8^2 \cdot 2$, so $\sqrt{128} = \sqrt{64 \cdot 2} = 8\sqrt{2}$

Now handle variables:
- $\sqrt{a^3} = \sqrt{a^2 \cdot a} = a\sqrt{a}$
- $\sqrt{b^4} = b^2$

Multiply all together:
$$
\sqrt{128 a^3 b^4} = 8\sqrt{2} \cdot a\sqrt{a} \cdot b^2 = 8ab^2 \sqrt{2a}
$$

✔ Option D: $8ab^2 \sqrt{2a}$

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3. Simplify:
$\sqrt{98}$

Factor 98:
$98 = 49 \cdot 2 = 7^2 \cdot 2$

So:
$$
\sqrt{98} = \sqrt{49 \cdot 2} = 7\sqrt{2}
$$

✔ Option B: $7\sqrt{2}$

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4. Simplify:
$\sqrt{180}$

Factor 180:
$180 = 36 \cdot 5 = 6^2 \cdot 5$

So:
$$
\sqrt{180} = \sqrt{36 \cdot 5} = 6\sqrt{5}
$$

✔ Option A: $6\sqrt{5}$

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5. Simplify:
$\sqrt{27 m^7 p^4}$

Break it down:
- $27 = 9 \cdot 3 = 3^2 \cdot 3$, so $\sqrt{27} = 3\sqrt{3}$
- $\sqrt{m^7} = \sqrt{m^6 \cdot m} = m^3 \sqrt{m}$
- $\sqrt{p^4} = p^2$

Multiply:
$$
\sqrt{27 m^7 p^4} = 3\sqrt{3} \cdot m^3 \sqrt{m} \cdot p^2 = 3m^3 p^2 \sqrt{3m}
$$

✔ Option B: $3m^3 p^2 \sqrt{3m}$

(Option A says $9m^3 p^2 \sqrt{3m}$ — too big; 9 is wrong because $\sqrt{27} = 3\sqrt{3}$, not $9\sqrt{3}$)

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Final Answer:
1. C
2. D
3. B
4. A
5. B