Question

1. express in simplest radical form: \\(sqrt{112}\\)
2. express in simplest radical form: \\(sqrt{147}\\)
3. express in simplest radical form: \\(sqrt{150}\\)
4. express in simplest radical form: \\(sqrt{27}\\)
5. express in simplest radical form: \\(sqrt{8}\\)

Explanation:

Problem 16:

Step1: Factor out perfect square

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

Step2: Split the square root

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

Step3: Simplify perfect square

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

Problem 17:

Step1: Factor out perfect square

$\sqrt{147} = \sqrt{49 \times 3}$

Step2: Split the square root

$\sqrt{49} \times \sqrt{3}$

Step3: Simplify perfect square

$7 \times \sqrt{3} = 7\sqrt{3}$

Problem 18:

Step1: Factor out perfect square

$\sqrt{150} = \sqrt{25 \times 6}$

Step2: Split the square root

$\sqrt{25} \times \sqrt{6}$

Step3: Simplify perfect square

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

Problem 19:

Step1: Factor out perfect square

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

Step2: Split the square root

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

Step3: Simplify perfect square

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

Problem 20:

Step1: Factor out perfect square

$\sqrt{8} = \sqrt{4 \times 2}$

Step2: Split the square root

$\sqrt{4} \times \sqrt{2}$

Step3: Simplify perfect square

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

Answer:

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