Question #0e278

Oct 13, 2016

$3 \sqrt{2} - 4 \sqrt{5}$

Explanation:

In this question, it was establish that $4 \sqrt{5} - 3 \sqrt{2}$ is a square root of $98 - \sqrt{10}$. To get the other square root, we can simply multiply by $- 1$.

Notice that for any $x$, we have

${x}^{2} = 1 {x}^{2} = {\left(- 1\right)}^{2} {x}^{2} = {\left(- x\right)}^{2}$

meaning that if $x$ is a square root of ${x}^{2}$, then so is $- x$. Applying that here, we get the other square root as

$- \left(4 \sqrt{5} - 3 \sqrt{2}\right) = 3 \sqrt{2} - 4 \sqrt{5}$