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?

#NumberTheory #PracticeProblems #HelpMe!

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 - 7 years, 8 months ago

square both sides and solve. you now have $a + 2\sqrt{ab} + b$

Kenneth Chan - 7 years, 8 months ago

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 - 7 years, 8 months ago

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 - 7 years, 8 months ago

aditya dev - 5 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$