kimberlyma
Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Get detailed and accurate answers to your questions from a dedicated 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 this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.