To determine which expression is equivalent to [tex]\(2 \sqrt{98} \cdot \sqrt{2}\)[/tex], let's work through the problem step by step.
First, we will use the properties of square roots and multiplication to simplify the expression.
1. Start with the given expression:
[tex]\[
2 \sqrt{98} \cdot \sqrt{2}
\][/tex]
2. Combine the square roots under a single radical using the property [tex]\(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\)[/tex]:
[tex]\[
2 \sqrt{98 \cdot 2}
\][/tex]
3. Multiply the numbers inside the square root:
[tex]\[
98 \cdot 2 = 196
\][/tex]
This simplifies the expression to:
[tex]\[
2 \sqrt{196}
\][/tex]
4. Recognize that 196 is a perfect square:
[tex]\[
\sqrt{196} = 14
\][/tex]
5. Substitute back into the expression:
[tex]\[
2 \sqrt{196} = 2 \cdot 14
\][/tex]
6. Perform the final multiplication:
[tex]\[
2 \cdot 14 = 28
\][/tex]
So, the equivalent expression to [tex]\(2 \sqrt{98} \cdot \sqrt{2}\)[/tex] is:
[tex]\[
28
\][/tex]
Thus, the answer is [tex]\( \boxed{28} \)[/tex].
