Simplify square root of 7(-8 square root of 10+ square root of 14)

$\sqrt{7} (- 8 \sqrt{10} + \sqrt{14})$

Apply the distributive property.

$\sqrt{7} (- 8 \sqrt{10}) + \sqrt{7} \sqrt{14}$

Multiply $\sqrt{7} (- 8 \sqrt{10})$ .

Combine using the product rule for radicals.

$- 8 \sqrt{7 \cdot 10} + \sqrt{7} \sqrt{14}$

Multiply $7$ by $10$ .

$- 8 \sqrt{70} + \sqrt{7} \sqrt{14}$

$- 8 \sqrt{70} + \sqrt{7} \sqrt{14}$

Combine using the product rule for radicals.

$- 8 \sqrt{70} + \sqrt{7 \cdot 14}$

Simplify each term.

Multiply $7$ by $14$ .

$- 8 \sqrt{70} + \sqrt{98}$

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

Factor $49$ out of $98$ .

$- 8 \sqrt{70} + \sqrt{49 (2)}$

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

$- 8 \sqrt{70} + \sqrt{7^{2} \cdot 2}$

$- 8 \sqrt{70} + \sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$- 8 \sqrt{70} + 7 \sqrt{2}$

$- 8 \sqrt{70} + 7 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$- 8 \sqrt{70} + 7 \sqrt{2}$

Decimal Form:

$- 57.03330718 \dots$

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