Question

1. express in simplest form: \\(sqrt{49}\\)
2. express in simplest radical form: \\(sqrt{45}\\)
3. express in simplest radical form: \\(sqrt{9}\\)
4. express in simplest radical form: \\(sqrt{54}\\)
5. express in simplest radical form: \\(sqrt{180}\\)

Explanation:

Step1: Factor into perfect square

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

Step2: Simplify the radical

$\sqrt{7^2} = 7$

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Step1: Factor into perfect square

$\sqrt{45} = \sqrt{9 \times 5} = \sqrt{3^2 \times 5}$

Step2: Simplify the radical

$\sqrt{3^2 \times 5} = 3\sqrt{5}$

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Step1: Factor into perfect square

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

Step2: Simplify the radical

$\sqrt{3^2} = 3$

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Step1: Factor into perfect square

$\sqrt{54} = \sqrt{9 \times 6} = \sqrt{3^2 \times 6}$

Step2: Simplify the radical

$\sqrt{3^2 \times 6} = 3\sqrt{6}$

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Step1: Factor into perfect square

$\sqrt{180} = \sqrt{36 \times 5} = \sqrt{6^2 \times 5}$

Step2: Simplify the radical

$\sqrt{6^2 \times 5} = 6\sqrt{5}$

Answer:

1. $7$
2. $3\sqrt{5}$
3. $3$
4. $3\sqrt{6}$
5. $6\sqrt{5}$