Simplifying Complex Square Root Expressions

The process of simplifying complex square root expressions is a fundamental skill in algebra and is essential for various mathematical and scientific applications. This article provides a detailed guide on how to simplify expressions involving square roots, using the expression 2√32 3√8 - 9√50 √98 as a case study.

Understanding the Expression

To begin, the given expression is 2√32 3√8 - 9√50 √98. The goal is to simplify each term and combine like terms to obtain the final simplified form. This process involves breaking down the numbers under the square root into their prime factors and simplifying as much as possible.

Step-by-Step Simplification

Simplifying √32

The first term to simplify is √32.

Step 1: Factor 32 to 16 times 2.

Step 2: Simplify √16, which is 4, and take it out of the square root.

Therefore, √32 4√2.

Applying the coefficient 2, we get 2√32 2times;4√2 8√2.

Simplifying √8

The next term to simplify is √8.

Step 1: Factor 8 to 4 times 2.

Step 2: Simplify √4, which is 2, and take it out of the square root.

Therefore, √8 2√2.

Applying the coefficient 3, we get 3√8 3times;2√2 6√2.

Simplifying √50

The next term to simplify is √50.

Step 1: Factor 50 to 25 times 2.

Step 2: Simplify √25, which is 5, and take it out of the square root.

Therefore, √50 5√2.

Applying the coefficient -9, we get -9√50 -9times;5√2 -45√2.

Simplifying √98

The last term to simplify is √98.

Step 1: Factor 98 to 49 times 2.

Step 2: Simplify √49, which is 7, and take it out of the square root.

Therefore, √98 7√2.

Combining the Simplified Terms

Now that all terms have been simplified, we can substitute them back into the original expression:

2√32 3√8 - 9√50 √98 8√2 6√2 - 45√2 7√2

Next, combine like terms:

8√2 6√2 - 45√2 7√2 (8 6 - 45 7)√2 -24√2

Conclusion

The simplified form of the expression 2√32 3√8 - 9√50 √98 is -24√2.

Related Keywords

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