Question

simplifying radicals review
name: aliyah washington
simplify each radical completely.

1. $sqrt{49}$
2. $sqrt{192}$
3. $9sqrt{64}$
4. $7sqrt{175}$

Explanation:

Step1: Simplify perfect square radical

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

Step2: Factor out perfect square from 192

$\sqrt{192} = \sqrt{64 \times 3} = \sqrt{8^2 \times 3}$

Step3: Separate and simplify radicals

$\sqrt{8^2 \times 3} = \sqrt{8^2} \times \sqrt{3} = 8\sqrt{3}$

Step4: Simplify radical then multiply

$9\sqrt{64} = 9 \times \sqrt{8^2} = 9 \times 8 = 72$

Step5: Factor out perfect square from 175

$7\sqrt{175} = 7 \times \sqrt{25 \times 7} = 7 \times \sqrt{5^2 \times 7}$

Step6: Separate, simplify, then multiply

$7 \times \sqrt{5^2} \times \sqrt{7} = 7 \times 5 \times \sqrt{7} = 35\sqrt{7}$

Answer:

1. $7$
2. $8\sqrt{3}$
3. $72$
4. $35\sqrt{7}$