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Determine the result of the following operation in its simplest form. $\newline$ $\sqrt{98}\times\sqrt{2}$

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Multiply radical expressions

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Q. Determine the result of the following operation in its simplest form.

\newline

\sqrt{98}\times\sqrt{2}

Find Prime Factorization: Find the prime factorization of $98$ , which is $2 \times 7 \times 7$ . So, $\sqrt{98}$ can be expressed as $\sqrt{2 \times 7^2}$ .
Apply Multiplication Property: Apply the multiplication property of square roots to $\sqrt{2 \times 7^2}$ $\times \sqrt{2}$ . So, $\sqrt{98} \times \sqrt{2} = \sqrt{2 \times 7^2 \times 2}$ .
Combine Like Terms: Combine the like terms under the square root. So, $\sqrt{2 \times 7^2 \times 2} = \sqrt{2^2 \times 7^2}$ .
Pull Out Square Factors: Pull out the square factors from the square root. So, $\sqrt{2^2 \times 7^2} = 2 \times 7$ .
Simplify Final Answer: Simplify $2 \times 7$ to get the final answer. So, $\sqrt{98} \times \sqrt{2} = 14$ .

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