Evaluate - square root of 6*(7 square root of 10)

$- \sqrt{6} \cdot (7 \sqrt{10})$

Step 1

Multiply $- \sqrt{6} (7 \sqrt{10})$ .

Multiply $7$ by $- 1$ .

$- 7 \sqrt{6} \sqrt{10}$

Combine using the product rule for radicals.

$- 7 \sqrt{10 \cdot 6}$

Multiply $10$ by $6$ .

$- 7 \sqrt{60}$

$- 7 \sqrt{60}$

Step 2

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$- 7 \sqrt{4 (15)}$

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

$- 7 \sqrt{2^{2} \cdot 15}$

$- 7 \sqrt{2^{2} \cdot 15}$

Step 3

Pull terms out from under the radical.

$- 7 (2 \sqrt{15})$

Step 4

Multiply $2$ by $- 7$ .

$- 14 \sqrt{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- 14 \sqrt{15}$

Decimal Form:

$- 54.22176684 \dots$

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