Question

Rationalize:
$8+2\sqrt{2}$
Answer: $2\sqrt{2}$

State true or false.

• A. True
• B. False

Answer 1

The correct option is B False

We rationalize $8+2\sqrt{2}$ as follows:

$\frac{8+2\sqrt{2}}{1}\times \frac{8-2\sqrt{2}}{8-2\sqrt{2}}=\frac{{\left(8\right)}^2-{\left(2\sqrt{2}\right)}^2}{8-2\sqrt{2}}\{\because (a-b)(a+b)=a^2-b^2\}=\frac{64-(4\times 2)}{8-2\sqrt{2}}=\frac{64-8}{8-2\sqrt{2}}$

$=\frac{56}{2(4-\sqrt{2})}=\frac{28}{4-\sqrt{2}}$

Hence, $8+2\sqrt{2}=\frac{28}{4-\sqrt{2}}$