Question

multiplying radicals

1. \\(\sqrt{20} \cdot \sqrt{12}\\)
2. \\(\sqrt{20} \cdot \sqrt{25}\\)
3. \\(7\sqrt{18} \cdot \sqrt{12}\\)
4. \\(-3\sqrt{10} \cdot -4\sqrt{6}\\)

answers
\\(42\sqrt{7}\\)
\\(10\sqrt{5}\\)
\\(24\sqrt{15}\\)
\\(4\sqrt{15}\\)
\\(42\sqrt{6}\\)

Explanation:

Step1: Simplify $\sqrt{20} \cdot \sqrt{12}$

Combine radicals, factor perfect squares:
$\sqrt{20 \cdot 12} = \sqrt{240} = \sqrt{16 \cdot 15} = 4\sqrt{15}$

Step2: Simplify $\sqrt{20} \cdot \sqrt{25}$

Combine radicals, simplify perfect squares:
$\sqrt{20 \cdot 25} = \sqrt{500} = \sqrt{100 \cdot 5} = 10\sqrt{5}$

Step3: Simplify $7\sqrt{18} \cdot \sqrt{12}$

Combine radicals, factor perfect squares:
$7\sqrt{18 \cdot 12} = 7\sqrt{216} = 7\sqrt{36 \cdot 6} = 7 \cdot 6\sqrt{6} = 42\sqrt{6}$

Step4: Simplify $-3\sqrt{10} \cdot -4\sqrt{6}$

Multiply coefficients, combine radicals:
$(-3 \cdot -4)\sqrt{10 \cdot 6} = 12\sqrt{60} = 12\sqrt{4 \cdot 15} = 12 \cdot 2\sqrt{15} = 24\sqrt{15}$

Answer:

1. $4\sqrt{15}$
2. $10\sqrt{5}$
3. $42\sqrt{6}$
4. $24\sqrt{15}$