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Chapter 0: Problem 41

Add or subtract terms whenever possible. $$3 \sqrt{18}+5 \sqrt{50}$$

Short Answer

Expert verified
The combination of the given terms is simplified to \(34\sqrt{2}\).

Step by step solution

01

Prime Factorization and Root Extraction

First, break down each term into prime numbers under the square root: \[3 \sqrt{18} = 3 \sqrt{9*2} = 3 * \sqrt{9} * \sqrt{2} = 3 * 3 * \sqrt{2} = 9\sqrt{2}\] Similarly, \[5 \sqrt{50} = 5 * \sqrt{25*2} = 5 * \sqrt{25} * \sqrt{2} = 5 * 5 * \sqrt{2} = 25\sqrt{2}\]
02

Combine Like Terms

The resulting expressions from step 1 now have common root terms (\(\sqrt{2}\)), and can be added together: \(9\sqrt{2} + 25\sqrt{2} = 34\sqrt{2}\).
03

Final Simplification

Since it's not possible to simplify the square root of 2 any further, then the final simplified version of the given expression is \(34\sqrt{2}\).

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