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?

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?

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

Consider the following question:

– Calvin Lin Staff · 3 years, 11 months agoLog in to reply

– Kenneth Chan · 3 years, 11 months ago

square both sides and solve. you now have \(a + 2\sqrt{ab} + b\)Log in to reply

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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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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