Question

How do I solve pic rel? Online calculators keep saying the result is -1 but they don't show any steps which is confusing

Answer 1

Answer:

-1

Step-by-step explanation:

$\sqrt{9 - 4 \sqrt{2} } - 2 \sqrt{2} \\ \\ = \sqrt{8 + 1 - 4 \sqrt{2} } - 2 \sqrt{2} \\ \\ = \sqrt{8 - 4 \sqrt{2} + 1} - 2 \sqrt{2} \\ \\ = \sqrt{ {(2 \sqrt{2}) }^{2} - 2 \times 2 \sqrt{2} \times 1 + {1}^{2} } - 2 \sqrt{2} \\ \\ = \sqrt{( {2 \sqrt{2} - 1)}^{2} } - 2 \sqrt{2} \\ \\ (2 \sqrt{2} - 1) - 2 \sqrt{2} \\ \\ = 2 \sqrt{2} - 1 - 2 \sqrt{2} \\ \\ = - 1$