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Chapter 5: Problem 47

Perform the indicated operation. Simplify the answer when possible. \(\sqrt{5}+\sqrt{20}\)

Short Answer

Expert verified
The simplified form of \(\sqrt{5} \+ \sqrt{20}\) is \(3*\sqrt{5}\).

Step by step solution

01

Simplify the roots

First, start with the square roots given in the problem. The \(\sqrt{5}\) is already simplified, but the \(\sqrt{20}\) can be simplified further. To do so, look for perfect squares that factor into 20. The largest perfect square that factors into 20 is 4. So, we can write \(\sqrt{20}\) as \(\sqrt{4*5}\).
02

Break down the roots

Now, remember a property of square roots: \(\sqrt{a*b} = \sqrt{a} * \sqrt{b}\). So the \(\sqrt{4*5}\) can be separated as \(\sqrt{4}*\sqrt{5}\). After calculating, we get \(2*\sqrt{5}\).
03

Add the roots

We now have to add \(\sqrt{5}\) and \(2*\sqrt{5}\). Since they are like terms, they can be added together. Doing so gives \(3*\sqrt{5}\).

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(-9,-5,-1,3, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(6,-6,-18,-30, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(2,6,10,14, \ldots\)

You will develop geometric sequences that model the population growth for California and Texas, the two most populated U.S. states. The table shows the population of California for 2000 and 2010 , with estimates given by the U.S. Census Bureau for 2001 through \(2009 .\) $$ \begin{array}{|l|l|l|l|l|l|l|} \hline \text { Year } & \mathbf{2 0 0 0} & \mathbf{2 0 0 1} & \mathbf{2 0 0 2} & \mathbf{2 0 0 3} & \mathbf{2 0 0 4} & \mathbf{2 0 0 5} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 33.87 & 34.21 & 34.55 & 34.90 & 35.25 & 35.60 \\ \hline \end{array} $$ $$ \begin{array}{|l|l|l|l|l|l|} \hline \text { Year } & \mathbf{2 0 0 6} & \mathbf{2 0 0 7} & \mathbf{2 0 0 8} & \mathbf{2 0 0 9} & \mathbf{2 0 1 0} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 36.00 & 36.36 & 36.72 & 37.09 & 37.25 \\ \hline \end{array} $$ a. Divide the population for each year by the population in the preceding year. Round to two decimal places and show that California has a population increase that is approximately geometric. b. Write the general term of the geometric sequence modeling California's population, in millions, \(n\) years after \(1999 .\) c. Use your model from part (b) to project California's population, in millions, for the year 2020 . Round to two decimal places.

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{4}\), when \(a_{1}=9, r=-\frac{1}{3}\).
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