Waste less time on Facebook — follow Brilliant.
×

\(\sqrt{\sqrt{\sqrt{\sqrt{4.\underbrace {00\dots}_{300}3}}}}\) = ?

Note by Yannawat Praserttham
1 year, 9 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. 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"
MathAppears 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

Sort by:

Top Newest

What are you looking for exactly? The simplest form of the answer? The first few digits of the number?

If you're looking for the first few digits of the number, try \((1+x)^n \approx 1 + nx\). for small \(x\).

Pi Han Goh - 1 year, 9 months ago

Log in to reply

The simplest form of the answer.

Yannawat Praserttham - 1 year, 9 months ago

Log in to reply

Hint: convert decimal number into an improper fraction.

Pi Han Goh - 1 year, 9 months ago

Log in to reply

@Pi Han Goh I did that, but i don't know what to do next.

Yannawat Praserttham - 1 year, 9 months ago

Log in to reply

@Yannawat Praserttham Show me what you've done so far.

Pi Han Goh - 1 year, 9 months ago

Log in to reply

@Pi Han Goh \(4.\underbrace {00\dots}_{300}3\) = \(\frac{(4 \times 10^{301})+3}{10^{301}}\)

= \(\frac{4 \times 10^{301}}{10^{301}}+\frac{3}{10^{301}}\)

= \(4+\frac{3}{10^{301}}\)

Yannawat Praserttham - 1 year, 9 months ago

Log in to reply

@Yannawat Praserttham Combine it into a single fraction, you have \( \dfrac{4\cdot 10^{301} + 3}{10^{301}} \). Notice that neither e numerator nor the denominator is not a perfect square (do you know how to prove that?), so your final answer is simply \( \left( \dfrac{4\cdot 10^{301} + 3}{10^{301}} \right)^{1/16} \).

Pi Han Goh - 1 year, 9 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...