Evaluate 5 square root of 3- square root of 98+ square root of 48+6 square root of 2

$5 \sqrt{3} - \sqrt{98} + \sqrt{48} + 6 \sqrt{2}$

Step 1

Simplify each term.

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

Factor $49$ out of $98$ .

$5 \sqrt{3} - \sqrt{49 (2)} + \sqrt{48} + 6 \sqrt{2}$

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

$5 \sqrt{3} - \sqrt{7^{2} \cdot 2} + \sqrt{48} + 6 \sqrt{2}$

Pull terms out from under the radical.

$5 \sqrt{3} - (7 \sqrt{2}) + \sqrt{48} + 6 \sqrt{2}$

Multiply $7$ by $- 1$ .

$5 \sqrt{3} - 7 \sqrt{2} + \sqrt{48} + 6 \sqrt{2}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$5 \sqrt{3} - 7 \sqrt{2} + \sqrt{16 (3)} + 6 \sqrt{2}$

Rewrite $16$ as $4^{2}$ .

$5 \sqrt{3} - 7 \sqrt{2} + \sqrt{4^{2} \cdot 3} + 6 \sqrt{2}$

Pull terms out from under the radical.

$5 \sqrt{3} - 7 \sqrt{2} + 4 \sqrt{3} + 6 \sqrt{2}$

Step 2

Simplify by adding terms.

Add $5 \sqrt{3}$ and $4 \sqrt{3}$ .

$9 \sqrt{3} - 7 \sqrt{2} + 6 \sqrt{2}$

Add $- 7 \sqrt{2}$ and $6 \sqrt{2}$ .

$9 \sqrt{3} - \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{3} - \sqrt{2}$

Decimal Form:

$14.17424370 \dots$