Question

name: camila balbc
period:
algebra unit 7 homework 4 - add & subtract radicals
directions: show all work in order to receive full credit.

1. what is the sum of $8\sqrt{3}$ and $\sqrt{3}$?
2. calculate the sum of $\sqrt{24}$ and $\sqrt{150}$
3. the expression $6\sqrt{50} - 6\sqrt{2}$ written in simplest radical form is..
4. simplify $\sqrt{28} - \sqrt{7}$
5. simplify: $\sqrt{48} + \sqrt{75} - \sqrt{27}$

Explanation:

Step1: Add like radicals

$8\sqrt{3} + \sqrt{3} = (8+1)\sqrt{3}$

Step2: Simplify the coefficient

$(8+1)\sqrt{3} = 9\sqrt{3}$

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Step1: Simplify each radical

$\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}$, $\sqrt{150} = \sqrt{25 \times 6} = 5\sqrt{6}$

Step2: Add like radicals

$2\sqrt{6} + 5\sqrt{6} = (2+5)\sqrt{6}$

Step3: Simplify the coefficient

$(2+5)\sqrt{6} = 7\sqrt{6}$

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Step1: Simplify $\sqrt{50}$

$\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$

Step2: Substitute and distribute

$6 \times 5\sqrt{2} - 6\sqrt{2} = 30\sqrt{2} - 6\sqrt{2}$

Step3: Subtract like radicals

$30\sqrt{2} - 6\sqrt{2} = (30-6)\sqrt{2}$

Step4: Simplify the coefficient

$(30-6)\sqrt{2} = 24\sqrt{2}$

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Step1: Simplify $\sqrt{28}$

$\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}$

Step2: Subtract like radicals

$2\sqrt{7} - \sqrt{7} = (2-1)\sqrt{7}$

Step3: Simplify the coefficient

$(2-1)\sqrt{7} = \sqrt{7}$

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Step1: Simplify all radicals

$\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}$, $\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$, $\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$

Step2: Combine like radicals

$4\sqrt{3} + 5\sqrt{3} - 3\sqrt{3} = (4+5-3)\sqrt{3}$

Step3: Simplify the coefficient

$(4+5-3)\sqrt{3} = 6\sqrt{3}$

Answer:

1. $9\sqrt{3}$
2. $7\sqrt{6}$
3. $24\sqrt{2}$
4. $\sqrt{7}$
5. $6\sqrt{3}$