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Simplify the expression to simplest radical form:

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

Enter the correct answer in the box:

Sagot :

GinnyAnswer
To simplify the given expression:
[tex]\[ \frac{6}{\sqrt{3}} \cdot \frac{\sqrt{2}}{\sqrt{3}} \][/tex]

First, let's rewrite the expression by combining the fractions:
[tex]\[ \frac{6 \cdot \sqrt{2}}{\sqrt{3} \cdot \sqrt{3}} \][/tex]

Next, let's simplify the denominator:

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

So the expression now is:
[tex]\[ \frac{6 \cdot \sqrt{2}}{3} \][/tex]

Let's simplify the fraction:

[tex]\[ \frac{6}{3} = 2 \][/tex]

Thus, the expression now is:
[tex]\[ 2 \cdot \sqrt{2} \][/tex]

Therefore, the simplified form of the expression [tex]\(\frac{6}{\sqrt{3}} \cdot \frac{\sqrt{2}}{\sqrt{3}}\)[/tex] is:
[tex]\[ 2\sqrt{2} \][/tex]
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