Simplify 5 square root of 24*2 square root of 28

$5 \sqrt{24} \cdot 2 \sqrt{28}$

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$5 \sqrt{4 (6)} \cdot (2 \sqrt{28})$

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

$5 \sqrt{2^{2} \cdot 6} \cdot (2 \sqrt{28})$

$5 \sqrt{2^{2} \cdot 6} \cdot (2 \sqrt{28})$

Pull terms out from under the radical.

$5 (2 \sqrt{6}) \cdot (2 \sqrt{28})$

Multiply $2$ by $5$ .

$10 \sqrt{6} \cdot (2 \sqrt{28})$

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$10 \sqrt{6} \cdot (2 \sqrt{4 (7)})$

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

$10 \sqrt{6} \cdot (2 \sqrt{2^{2} \cdot 7})$

$10 \sqrt{6} \cdot (2 \sqrt{2^{2} \cdot 7})$

Pull terms out from under the radical.

$10 \sqrt{6} \cdot (2 (2 \sqrt{7}))$

Multiply $2$ by $2$ .

$10 \sqrt{6} \cdot (4 \sqrt{7})$

Multiply $10 \sqrt{6} (4 \sqrt{7})$ .

Multiply $4$ by $10$ .

$40 \sqrt{6} \sqrt{7}$

Combine using the product rule for radicals.

$40 \sqrt{7 \cdot 6}$

Multiply $7$ by $6$ .

$40 \sqrt{42}$

$40 \sqrt{42}$

The result can be shown in multiple forms.

Exact Form:

$40 \sqrt{42}$

Decimal Form:

$259.22962793 \dots$

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