Simplify √72 - √32 + √18
Understand the Problem
The question is asking us to simplify the expression involving square roots. We will break down each square root into its prime factors to simplify it further.
Answer
$5\sqrt{2}$
Answer for screen readers
The simplified form of the square root expression is $5\sqrt{2}$.
Steps to Solve
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Identify the square roots
Look at the expression and identify which square roots need to be simplified. For example, if you have $\sqrt{50}$, it can be broken down into its prime factors. -
Break down the square roots
Rewrite each square root in terms of its prime factors. For example: $$ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} $$ -
Simplify the square roots
Simplify the square root of each factor. For example: $$ \sqrt{25} = 5 $$ So, we have: $$ \sqrt{50} = 5\sqrt{2} $$ -
Combine the simplified terms
If there are multiple square roots in the expression, repeat the simplification and then combine all simplified terms together. -
Final expression
Write the complete simplified expression neatly.
The simplified form of the square root expression is $5\sqrt{2}$.
More Information
When simplifying square roots, breaking them down into their prime factors allows us to simplify them more easily. Additionally, this method is valuable because it applies to any composite number under a square root.
Tips
- Forgetting to include all factors when breaking down square roots. Always carefully factor each number completely.
- Not simplifying fully. Ensure that each square root is fully simplified before combining terms.
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