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Indices and Surds Practice

On a practice problem for indices and surds, an explanation was given that \[\sqrt{128 \pm 2\sqrt{847}}=\sqrt{121} \pm \sqrt{7}\]

I was not able to make that leap in my mind. Any help?

Note by Steve Gewinner
3 years, 11 months ago

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Note that the link you provided is unique to you, so I have removed it.

Consider the following question:

Can you find integers values of \(a\) and \(b\) such that \( \sqrt{ 128 + 2 \sqrt{847} } = \sqrt{a} + \sqrt{b}\)?

Calvin Lin Staff · 3 years, 11 months ago

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@Calvin Lin square both sides and solve. you now have \(a + 2\sqrt{ab} + b\) Kenneth Chan · 3 years, 11 months ago

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36 Aditya Dev · 1 year, 11 months ago

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Thanks a lot. Next question, what am I missing from my formatting? Here's how I made the leap:

Like Kenneth mentioned, I looked for what would give me \(\sqrt{(\sqrt{a}+\sqrt{b})^{2}} = \sqrt{a+b+2\sqrt{ab}}\). So now it's clear to me that \[ \sqrt{128+2\sqrt{847}} = \sqrt{121+7+2\sqrt{121*7}} = \sqrt{(\sqrt{121}+\sqrt{7})^{2}} \] Steve Gewinner · 3 years, 11 months ago

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@Steve Gewinner You just need to add brackets around them, e.g. \( \backslash ( \text{ math code } \backslash) \) for inline text, and \( \backslash[ \text{ math code } \backslash ] \) for code to take up it's own line.

I've added the brackets to your comment, so you can click on edits to see it. Otherwise, your math code is good.

You can see math formatting guide for more details. Calvin Lin Staff · 3 years, 11 months ago

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