Question

1 compound calculate and write the answer in its simplest form. 1. \\( \sqrt{15} \times \sqrt{35} = \\) \\( \quad \\) 2. \\( \sqrt{6} \times \sqrt{18} = \\) \\( \quad \\) 3. \\( 3\sqrt{2} \times \sqrt{6} = \\) \\( \quad \\)

Explanation:

Step1: Factor radicands

$\sqrt{15} \times \sqrt{35} = \sqrt{3 \times 5} \times \sqrt{5 \times 7}$

Step2: Combine square roots

$= \sqrt{3 \times 5 \times 5 \times 7}$

Step3: Simplify perfect squares

$= \sqrt{5^2 \times 21} = 5\sqrt{21}$

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Step1: Factor radicands

$\sqrt{6} \times \sqrt{18} = \sqrt{6} \times \sqrt{6 \times 3}$

Step2: Combine square roots

$= \sqrt{6 \times 6 \times 3}$

Step3: Simplify perfect squares

$= \sqrt{6^2 \times 3} = 6\sqrt{3}$

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Step1: Factor radicands

$3\sqrt{2} \times \sqrt{6} = 3\sqrt{2} \times \sqrt{2 \times 3}$

Step2: Combine square roots

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

Step3: Simplify perfect squares

$= 3\sqrt{2^2 \times 3} = 3 \times 2\sqrt{3} = 6\sqrt{3}$

Answer:

1. $5\sqrt{21}$
2. $6\sqrt{3}$
3. $6\sqrt{3}$