# How do you simplify (3+sqrt32)-(4+2sqrt98)?

May 10, 2018

$- 1 - 10 \sqrt{2}$

#### Explanation:

Original Question: $\left(3 + \sqrt{32}\right) - \left(4 + 2 \sqrt{98}\right)$

Distribute the negative so you have:
$3 + \sqrt{32} - 4 - 2 \sqrt{98} = - 1 + \sqrt{32} - 2 \sqrt{98}$

$- 1 + \sqrt{16 \times 2} - 2 \sqrt{49 \times 2}$
$= - 1 + \sqrt{{4}^{2} \times 2} - 2 \sqrt{{7}^{2} \times 2}$
$= - 1 + \sqrt{{4}^{2}} \cdot \sqrt{2} - 2 \sqrt{{7}^{2}} \cdot \sqrt{2}$
$= - 1 + 4 \sqrt{2} - 2 \cdot 7 \sqrt{2}$
$= - 1 + 4 \sqrt{2} - 14 \sqrt{2}$
Since $4 \sqrt{2}$ and $- 14 \sqrt{2}$, we can subtract the two terms.
$= - 1 - 10 \sqrt{2}$