Answer: [tex]-\sqrt{7}[/tex]
Negative square root of 7, or in shorthand, -sqrt(7)
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Explanation:
Let's first simplify [tex]\sqrt{63}[/tex]
Note how 63 = 9*7, and 9 is the largest perfect square factor. This is to help simplify the root as such:
[tex]\sqrt{63} = \sqrt{9*7}\\\\\sqrt{63} = \sqrt{9}*\sqrt{7}\\\\\sqrt{63} = 3\sqrt{7}[/tex]
Therefore, we can say,
[tex]\sqrt{63}-4\sqrt{7}\\\\3\sqrt{7}-4\sqrt{7}\\\\(3-4)\sqrt{7}\\\\-1*\sqrt{7}\\\\-\sqrt{7}\\\\[/tex]
If you want, you can think of [tex]x = \sqrt{7}[/tex] to get
[tex]3\sqrt{7}-4\sqrt{7} = 3x-4x = -1x = -\sqrt{7}\\\\[/tex]
