kimberlyma
Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

What is the smallest integer $n$ such that $n\sqrt{2}$ is greater than $20$? (Note: $n\sqrt{2}$ means $n$ times $\sqrt{2}$.)

Sagot :

Question:

What is the smallest integer [tex]$n$[/tex] such that [tex]$n\sqrt{2}$[/tex] is greater than [tex]$20$[/tex]? (Note: [tex]$n\sqrt{2}$[/tex] means [tex]$n$[/tex] times [tex]$\sqrt{2}$[/tex].)

Solution:

  • n√2 > 20
  • => n > 20/√2
  • => n > 4 x 5/√2
  • => n > 2 x 2 x 5/√2
  • => n > √4 x √4 x √25/√2
  • => n > √2 x √4 x √25
  • => n > √2 x 4 x 25
  • => n > 10√2
  • => n > 14.14 (Rounded)

Smallest integer possibility for n is 15.

Hence, the smallest possible integer is 11.

Answer:

15

Step-by-step explanation:

In order to compare $n\sqrt{2}$ to $20$, we can compare the square of $n\sqrt{2}$ to the square of $20.$ We have

\begin{align*}

\left(n\sqrt{2}\right)^2 &= \left(n\sqrt{2}\right)\left(n\sqrt{2}\right) = n^2 \left(\sqrt{2}\right)^2 = n^2\cdot 2= 2n^2,\\

20^2 &= 400.

\end{align*}Therefore, we have $n\sqrt{2} > 20$ whenever $n^2 > 200.$ Since $14^2 = 196$ and $15^2 = 225,$ we know that $\boxed{15}$ is the smallest integer $n$ such that $n\sqrt{2}$ is greater than $20.$

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.