Simplifying Radical Expressions worksheet with 14 algebraic problems to solve.

Final Answer:
1) $5\sqrt{5n}$
2) $6\sqrt{6v}$
3) $24k\sqrt{2}$
4) $8m\sqrt{8m}$ → $8m \cdot 2\sqrt{2m} = 16m\sqrt{2m}$
Wait — let’s simplify each correctly, step by step, to avoid mistakes.

Actually, better to compute each fully simplified:

1) $\sqrt{125n} = \sqrt{25 \cdot 5n} = 5\sqrt{5n}$
2) $\sqrt{216v} = \sqrt{36 \cdot 6v} = 6\sqrt{6v}$
3) $\sqrt{512k^2} = \sqrt{256 \cdot 2 \cdot k^2} = 16k\sqrt{2}$
4) $\sqrt{512m^3} = \sqrt{256 \cdot 2 \cdot m^2 \cdot m} = 16m\sqrt{2m}$
5) $\sqrt{216k^4} = \sqrt{36 \cdot 6 \cdot k^4} = 6k^2\sqrt{6}$
6) $\sqrt{100v^3} = \sqrt{100 \cdot v^2 \cdot v} = 10v\sqrt{v}$
7) $\sqrt{80p^3} = \sqrt{16 \cdot 5 \cdot p^2 \cdot p} = 4p\sqrt{5p}$
8) $\sqrt{45p^2} = \sqrt{9 \cdot 5 \cdot p^2} = 3p\sqrt{5}$
9) $\sqrt{147m^3} = \sqrt{49 \cdot 3 \cdot m^2 \cdot m} = 7m\sqrt{3m}$
10) $\sqrt{100m^4} = \sqrt{100 \cdot (m^2)^2} = 10m^2$
11) $\sqrt{75x^2} = \sqrt{25 \cdot 3 \cdot x^2} = 5x\sqrt{3}$
12) $\sqrt{64m^4} = \sqrt{64 \cdot (m^2)^2} = 8m^2$
13) $\sqrt{16u^4} = \sqrt{16 \cdot (u^2)^2} = 4u^2$
14) $\sqrt{28x^3} = \sqrt{4 \cdot 7 \cdot x^2 \cdot x} = 2x\sqrt{7x}$

So the final answers are:

1) $5\sqrt{5n}$
2) $6\sqrt{6v}$
3) $16k\sqrt{2}$
4) $16m\sqrt{2m}$
5) $6k^2\sqrt{6}$
6) $10v\sqrt{v}$
7) $4p\sqrt{5p}$
8) $3p\sqrt{5}$
9) $7m\sqrt{3m}$
10) $10m^2$
11) $5x\sqrt{3}$
12) $8m^2$
13) $4u^2$
14) $2x\sqrt{7x}$