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Chapter 5: Problem 91

Explain how to add \(\sqrt{3}+\sqrt{12}\).

Short Answer

Expert verified
The solution is \(3\sqrt{3}\)

Step by step solution

01

Simplify \(\sqrt{12}\)

First, we need to simplify \(\sqrt{12}\). This can be done by looking for factors of 12 that are perfect squares. The number 4 is such a factor because it is a square of 2. Therefore, we can rewrite \(\sqrt{12}\) as \(\sqrt{4} \cdot \(\sqrt{3}\), which simplifies to \(2\sqrt{3}\).
02

Perform the Addition

With \(\sqrt{3}\) and \(2\sqrt{3}\) in simplified form, adding these two terms together is relatively straightforward, by simply adding the coefficients of the 'like terms'. 'Like terms' refers to terms that have the same variable and exponent. Here, the variable is \(\sqrt{3}\). Therefore, \( \sqrt{3} + 2\sqrt{3} = 3\sqrt{3}\)

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Most popular questions from this chapter

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(12,6,3, \frac{3}{2}, \ldots\)

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(18,6,2, \frac{2}{3}, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(3,8,13,18, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{6}\), when \(a_{1}=-2, r=-3\).

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If a sequence is geometric, we can write as many terms as we want by repeatedly multiplying by the common ratio.
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