Waste less time on Facebook — follow Brilliant.
×

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

Note by Yannawat Praserttham
9 months, 4 weeks ago

No vote yet
1 vote

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 · 9 months, 4 weeks ago

Log in to reply

@Pi Han Goh The simplest form of the answer. Yannawat Praserttham · 9 months, 4 weeks ago

Log in to reply

@Yannawat Praserttham Hint: convert decimal number into an improper fraction. Pi Han Goh · 9 months, 3 weeks ago

Log in to reply

@Pi Han Goh I did that, but i don't know what to do next. Yannawat Praserttham · 9 months, 3 weeks ago

Log in to reply

@Yannawat Praserttham Show me what you've done so far. Pi Han Goh · 9 months, 3 weeks 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 · 9 months, 3 weeks 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 · 9 months, 3 weeks ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...