Which expression is equivalent to [tex]$2 \sqrt{98} \cdot \sqrt{2}$[/tex]?

A. [tex]$14 \sqrt{2}$[/tex]
B. 28
C. [tex][tex]$4 \sqrt{98}$[/tex][/tex]
D. 784



Answer :

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].