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Chapter 5: Problem 56

Perform the indicated operation. Simplify the answer when possible. \(2 \sqrt{72}+3 \sqrt{50}-\sqrt{128}\)

Short Answer

Expert verified
The simplified version is \(19\sqrt{2}\).

Step by step solution

01

Simplify \(\sqrt{72}\)

Simplify \(\sqrt{72}\) by breaking it down into its prime factors, i.e., \(\sqrt{2^3*3^2}\). Then, bring out the perfect squares \((2,3)\) to get \(6\sqrt{2}\) as the simplest form.
02

Simplify \(\sqrt{50}\)

Similarly, simplify \(\sqrt{50}\) into \(\sqrt{2*5^2}\). Thereby, simplifying it results in \(5\sqrt{2}\).
03

Simplify \(\sqrt{128}\)

Simplify \(\sqrt{128}\) by breaking it down into \(\sqrt{2^7}\). Bring out the perfect squares \(2^3\) to get \(8\sqrt{2}\) as the simplest form.
04

Substitute the simplified square roots

Substitute the square roots in the initial expression: \(2*6\sqrt{2} + 3*5\sqrt{2} - 8\sqrt{2}\). This results in \(12\sqrt{2} + 15\sqrt{2} - 8\sqrt{2}\).
05

Combine the like terms

Combine the like terms to get the final simplified expression. Hence, \(12\sqrt{2} + 15\sqrt{2} - 8\sqrt{2} = 19\sqrt{2}\).

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