Question

1. $sqrt{18}$
2. $sqrt{96}$
3. $sqrt{72}$
4. $sqrt{48}$
5. $sqrt{98}$
6. $sqrt{27}$
7. $sqrt{294}$
8. $sqrt{112}$
9. $sqrt{180}$
10. $sqrt{144}$
11. $sqrt{112}$
12. $sqrt{245}$

Explanation:

Step1: Factor out perfect squares

$\sqrt{18} = \sqrt{9 \times 2}$

Step2: Simplify using $\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{9} \times \sqrt{2} = 3\sqrt{2}$

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Step1: Factor out perfect squares

$\sqrt{96} = \sqrt{16 \times 6}$

Step2: Simplify using $\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{16} \times \sqrt{6} = 4\sqrt{6}$

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Step1: Factor out perfect squares

$\sqrt{72} = \sqrt{36 \times 2}$

Step2: Simplify using $\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{36} \times \sqrt{2} = 6\sqrt{2}$

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Step1: Factor out perfect squares

$\sqrt{48} = \sqrt{16 \times 3}$

Step2: Simplify using $\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{16} \times \sqrt{3} = 4\sqrt{3}$

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Step1: Factor out perfect squares

$\sqrt{98} = \sqrt{49 \times 2}$

Step2: Simplify using $\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{49} \times \sqrt{2} = 7\sqrt{2}$

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Step1: Factor out perfect squares

$\sqrt{27} = \sqrt{9 \times 3}$

Step2: Simplify using $\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{9} \times \sqrt{3} = 3\sqrt{3}$

---

Step1: Factor out perfect squares

$\sqrt{294} = \sqrt{49 \times 6}$

Step2: Simplify using $\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{49} \times \sqrt{6} = 7\sqrt{6}$

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Step1: Factor out perfect squares

$\sqrt{112} = \sqrt{16 \times 7}$

Step2: Simplify using $\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{16} \times \sqrt{7} = 4\sqrt{7}$

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Step1: Factor out perfect squares

$\sqrt{180} = \sqrt{36 \times 5}$

Step2: Simplify using $\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{36} \times \sqrt{5} = 6\sqrt{5}$

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Step1: Simplify perfect square root

$\sqrt{144} = 12$

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Step1: Factor out perfect squares

$\sqrt{112} = \sqrt{16 \times 7}$

Step2: Simplify using $\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{16} \times \sqrt{7} = 4\sqrt{7}$

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Step1: Factor out perfect squares

$\sqrt{245} = \sqrt{49 \times 5}$

Step2: Simplify using $\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{49} \times \sqrt{5} = 7\sqrt{5}$

Answer:

1. $3\sqrt{2}$
2. $4\sqrt{6}$
3. $6\sqrt{2}$
4. $4\sqrt{3}$
5. $7\sqrt{2}$
6. $3\sqrt{3}$
7. $7\sqrt{6}$
8. $4\sqrt{7}$
9. $6\sqrt{5}$
10. $12$
11. $4\sqrt{7}$
12. $7\sqrt{5}$