martinezadam576
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What is this expression in simplified form?
[tex]\[
(6 \sqrt{2})(-3 \sqrt{5})
\][/tex]

A. -90
B. [tex]\(-18 \sqrt{10}\)[/tex]
C. [tex]\(-18 \sqrt{7}\)[/tex]
D. [tex]\(3 \sqrt{7}\)[/tex]

Sagot :

GinnyAnswer
To simplify the expression [tex]\((6 \sqrt{2})(-3 \sqrt{5})\)[/tex], we can follow these steps:

1. Separate the constants and the radicals:
[tex]\[ (6 \sqrt{2})(-3 \sqrt{5}) = (6 \cdot -3) \cdot (\sqrt{2} \cdot \sqrt{5}) \][/tex]

2. Multiply the constants:
[tex]\[ 6 \cdot -3 = -18 \][/tex]

3. Multiply the radicals:
[tex]\[ \sqrt{2} \cdot \sqrt{5} = \sqrt{2 \cdot 5} = \sqrt{10} \][/tex]

4. Combine the results:
[tex]\[ -18 \cdot \sqrt{10} \][/tex]

Therefore, the expression [tex]\((6 \sqrt{2})(-3 \sqrt{5})\)[/tex] simplifies to [tex]\(-18 \sqrt{10}\)[/tex].

The correct answer is:
B. [tex]\(-18 \sqrt{10}\)[/tex]
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