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Evaluate $\sqrt{98} / 2^{\frac{1}{2}}$

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Evaluate expressions using exponent rules

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Q. Evaluate

\sqrt{98} / 2^{\frac{1}{2}}

Simplify $\sqrt{98}$ : Simplify $\sqrt{98}$ . To simplify $\sqrt{98}$ , we need to find the prime factorization of $98$ and identify any square factors. $98 = 2 \times 49$ $49$ is a square number ( $7^2$ ), so we can take the square root of $49$ . $\sqrt{98} = \sqrt{2 \times 49}$ $\sqrt{98} = \sqrt{2} \times \sqrt{49}$ $\sqrt{98} = \sqrt{2} \times 7$
Simplify $2^{\frac{1}{2}}$ : Simplify $2^{\frac{1}{2}}$ . The expression $2^{\frac{1}{2}}$ is another way of writing the square root of $2$ . $2^{\frac{1}{2}} = \sqrt{2}$
Divide $\sqrt{98}$ by $2^{\frac{1}{2}}$ : Divide $\sqrt{98}$ by $2^{\frac{1}{2}}$ .
Now we divide $\sqrt{98}$ by $2^{\frac{1}{2}}$ , which is the same as $\sqrt{98} / \sqrt{2}$ .
$\sqrt{98} / 2^{\frac{1}{2}} = (\sqrt{2} \times 7) / \sqrt{2}$
Since $\sqrt{2}$ is present in both the numerator and the denominator, they cancel each other out.
$(\sqrt{2} \times 7) / \sqrt{2} = 7$

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