Question

examples 1–4
simplify each expression.

1. \\(\sqrt{52}\\)
2. \\(\sqrt{56}\\)
3. \\(\sqrt{72}\\)
4. \\(\sqrt{162}\\)
5. \\(\sqrt{243}\\)
6. \\(\sqrt{245}\\)

Explanation:

Step1: Factor out perfect square (√52)

$\sqrt{52} = \sqrt{4 \times 13}$

Step2: Simplify perfect square root

$\sqrt{4 \times 13} = \sqrt{4} \times \sqrt{13} = 2\sqrt{13}$

Step3: Factor out perfect square (√56)

$\sqrt{56} = \sqrt{4 \times 14}$

Step4: Simplify perfect square root

$\sqrt{4 \times 14} = \sqrt{4} \times \sqrt{14} = 2\sqrt{14}$

Step5: Factor out perfect square (√72)

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

Step6: Simplify perfect square root

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

Step7: Factor out perfect square (√162)

$\sqrt{162} = \sqrt{81 \times 2}$

Step8: Simplify perfect square root

$\sqrt{81 \times 2} = \sqrt{81} \times \sqrt{2} = 9\sqrt{2}$

Step9: Factor out perfect square (√243)

$\sqrt{243} = \sqrt{81 \times 3}$

Step10: Simplify perfect square root

$\sqrt{81 \times 3} = \sqrt{81} \times \sqrt{3} = 9\sqrt{3}$

Step11: Factor out perfect square (√245)

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

Step12: Simplify perfect square root

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

Answer:

1. $2\sqrt{13}$
2. $2\sqrt{14}$
3. $6\sqrt{2}$
4. $9\sqrt{2}$
5. $9\sqrt{3}$
6. $7\sqrt{5}$