Question #0e278

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Question #0e278

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Answer 1 · 2016-10-13T14:36:48

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

Explanation:

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

Notice that for any $x$ $x$ , we have

$x^{2} = 1 x^{2} = {(- 1)}^{2} x^{2} = {(- x)}^{2}$ $x^2 = 1x^2 = (-1)^2x^2 = (-x)^2$

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

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

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Question #0e278

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