Question

assignment 7.5

1. express in simplest radical form: √36
2. express in simplest radical form: √28
3. express in simplest radical form: √24
4. express in simplest radical form: √75
5. express in simplest radical form: √48
6. express in simplest radical form: √18
7. express in simplest radical form: √32
8. express in simplest radical form: √72
9. express in simplest radical form: √160
10. express in simplest radical form: √12

Explanation:

Step1: Factor out perfect square

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

Step2: Simplify the radical

$\sqrt{6^2} = 6$

Step1: Factor out perfect square

$\sqrt{28} = \sqrt{4 \times 7}$

Step2: Split & simplify radical

$\sqrt{4 \times 7} = \sqrt{2^2} \times \sqrt{7} = 2\sqrt{7}$

Step1: Factor out perfect square

$\sqrt{24} = \sqrt{4 \times 6}$

Step2: Split & simplify radical

$\sqrt{4 \times 6} = \sqrt{2^2} \times \sqrt{6} = 2\sqrt{6}$

Step1: Factor out perfect square

$\sqrt{75} = \sqrt{25 \times 3}$

Step2: Split & simplify radical

$\sqrt{25 \times 3} = \sqrt{5^2} \times \sqrt{3} = 5\sqrt{3}$

Step1: Factor out perfect square

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

Step2: Split & simplify radical

$\sqrt{16 \times 3} = \sqrt{4^2} \times \sqrt{3} = 4\sqrt{3}$

Step1: Factor out perfect square

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

Step2: Split & simplify radical

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

Step1: Factor out perfect square

$\sqrt{32} = \sqrt{16 \times 2}$

Step2: Split & simplify radical

$\sqrt{16 \times 2} = \sqrt{4^2} \times \sqrt{2} = 4\sqrt{2}$

Step1: Factor out perfect square

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

Step2: Split & simplify radical

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

Step1: Factor out perfect square

$\sqrt{160} = \sqrt{16 \times 10}$

Step2: Split & simplify radical

$\sqrt{16 \times 10} = \sqrt{4^2} \times \sqrt{10} = 4\sqrt{10}$

Step1: Factor out perfect square

$\sqrt{12} = \sqrt{4 \times 3}$

Step2: Split & simplify radical

$\sqrt{4 \times 3} = \sqrt{2^2} \times \sqrt{3} = 2\sqrt{3}$

Answer:

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