Simplify 5 square root of 98-3 square root of 6*5 square root of 3

$5 \sqrt{98} - 3 \sqrt{6} \cdot 5 \sqrt{3}$

Simplify each term.

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

Factor $49$ out of $98$ .

$5 \sqrt{49 (2)} - 3 \sqrt{6} \cdot (5 \sqrt{3})$

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

$5 \sqrt{7^{2} \cdot 2} - 3 \sqrt{6} \cdot (5 \sqrt{3})$

Pull terms out from under the radical.

$5 (7 \sqrt{2}) - 3 \sqrt{6} \cdot (5 \sqrt{3})$

Multiply $7$ by $5$ .

$35 \sqrt{2} - 3 \sqrt{6} \cdot (5 \sqrt{3})$

Multiply $- 3 \sqrt{6} (5 \sqrt{3})$ .

Multiply $5$ by $- 3$ .

$35 \sqrt{2} - 15 \sqrt{6} \sqrt{3}$

Combine using the product rule for radicals.

$35 \sqrt{2} - 15 \sqrt{3 \cdot 6}$

Multiply $3$ by $6$ .

$35 \sqrt{2} - 15 \sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$35 \sqrt{2} - 15 \sqrt{9 (2)}$

Rewrite $9$ as $3^{2}$ .

$35 \sqrt{2} - 15 \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$35 \sqrt{2} - 15 (3 \sqrt{2})$

Multiply $3$ by $- 15$ .

$35 \sqrt{2} - 45 \sqrt{2}$

Subtract $45 \sqrt{2}$ from $35 \sqrt{2}$ .

$- 10 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$- 10 \sqrt{2}$

Decimal Form:

$- 14.14213562 \dots$