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Chapter 5: Problem 52

Perform the indicated operation. Simplify the answer when possible. \(4 \sqrt{12}+2 \sqrt{75}\)

Short Answer

Expert verified
The simplified form of the expression is \(18\sqrt{3}\).

Step by step solution

01

Express as product of perfect square

First, we express each term as the product of a perfect square and a number. We can write \(\sqrt{12}\) as \(\sqrt{4*3}\) and \(\sqrt{75}\) as \(\sqrt{25*3}\). So, our expression becomes \(4*\sqrt{4*3} + 2*\sqrt{25*3}\).
02

Simplify square roots

The square root of a perfect square can be taken out of the root. So, \(\sqrt{4*3}\) becomes \(2*\sqrt{3}\) and \(\sqrt{25*3}\) becomes \(5*\sqrt{3}\). Our expression then becomes \(4*2*\sqrt{3} + 2*5\sqrt{3}\).
03

Combine like terms

Next, we combine the like terms. The like terms are those that involve \(\sqrt{3}\). So, our expression becomes \(8\sqrt{3} + 10\sqrt{3}\).
04

Simplify numbers

Finally, we simplify the numbers. The sum of 8 and 10 is 18. Therefore, our simplified expression is \(18\sqrt{3}\).

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(7,-7,7,-7, \ldots\)

Write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20 th term of the sequence. \(a_{1}=9, d=2\)

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

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=10, r=-4\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\sqrt{3}, 3,3 \sqrt{3}, 9, \ldots\)
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