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Evaluate square root of 8- square root of 98

$\sqrt{8} - \sqrt{98}$

Step 1

Simplify each term.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2)} - \sqrt{98}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 2} - \sqrt{98}$

$\sqrt{2^{2} \cdot 2} - \sqrt{98}$

Pull terms out from under the radical.

$2 \sqrt{2} - \sqrt{98}$

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$2 \sqrt{2} - \sqrt{49 (2)}$

Rewrite $49$ as $7^{2}$ .

$2 \sqrt{2} - \sqrt{7^{2} \cdot 2}$

$2 \sqrt{2} - \sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$2 \sqrt{2} - (7 \sqrt{2})$

Multiply $7$ by $- 1$ .

$2 \sqrt{2} - 7 \sqrt{2}$

$2 \sqrt{2} - 7 \sqrt{2}$

Step 2

Subtract $7 \sqrt{2}$ from $2 \sqrt{2}$ .

$- 5 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 5 \sqrt{2}$

Decimal Form:

$- 7.07106781 \dots$

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