I don't understand how I could calculate this:
$3\sqrt2 - \sqrt{32} + \sqrt{\dfrac{80}{16}}$
My answer is $-\sqrt2 + \sqrt5$, but the real answer should be $\dfrac{9-4\sqrt2}{4}$.
Answer
As commenters pointed out, $80$ should be $81$. The radicals simplify as follows:
$$
3\sqrt2 - \sqrt{32} + \sqrt{\dfrac{81}{16}} =
3\sqrt{2}- \sqrt{16} \sqrt{2} +\frac94 = (3-4)\sqrt{2}+\frac94 = \frac94-\sqrt{2}
$$
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