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Simplify the expression to simplest radical form.

[tex]\(\frac{6}{\sqrt{3}} \cdot \frac{\sqrt{2}}{\sqrt{3}}\)[/tex]

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Sagot :

GinnyAnswer
Let's simplify the given expression step-by-step:

[tex]\[ \frac{6}{\sqrt{3}} \cdot \frac{\sqrt{2}}{\sqrt{3}} \][/tex]

First, simplify inside the radicals:

Multiply the two fractions:

[tex]\[ \frac{6 \cdot \sqrt{2}}{\sqrt{3} \cdot \sqrt{3}} \][/tex]

Next, simplify the denominator:

[tex]\[ \sqrt{3} \cdot \sqrt{3} = 3 \][/tex]

So the expression becomes:

[tex]\[ \frac{6 \cdot \sqrt{2}}{3} \][/tex]

Simplify the fraction:

[tex]\[ 6 \div 3 = 2 \][/tex]

Thus, the simplest radical form of the expression is:

[tex]\[ 2 \cdot \sqrt{2} \][/tex]

This is the correct simplified form:

[tex]\[ \boxed{2 \cdot \sqrt{2}} \][/tex]
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