How to rewrite a radical?
Understand the Problem
The question is asking how to simplify or alter a radical expression. This involves understanding the rules of exponents and how to manipulate square roots or other roots algebraically.
Answer
$5\sqrt{2}$
Answer for screen readers
The simplified form of $\sqrt{50}$ is $5\sqrt{2}$.
Steps to Solve
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Identify the radical expression Start with the radical expression you want to simplify. For example, if you have $\sqrt{50}$, identify the number under the square root.
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Factor the number under the radical Find the prime factorization of $50$. You can break it down as follows: $$ 50 = 25 \times 2 $$
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Use the property of square roots Apply the property of square roots that states $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$. So, you can rewrite the expression: $$ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \cdot \sqrt{2} $$
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Simplify the square roots Now simplify each square root. The square root of $25$ is $5$: $$ \sqrt{25} = 5 $$
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Write the final simplified form Now combine the results: $$ \sqrt{50} = 5\sqrt{2} $$
The simplified form of $\sqrt{50}$ is $5\sqrt{2}$.
More Information
The process of simplifying radicals often involves factoring the number under the root to find perfect squares or cubes. This technique is helpful in various mathematical applications, from algebra to calculus.
Tips
- Forgetting to look for pairs in prime factorization can lead to an incomplete simplification.
- Misapplying the property of square roots, such as incorrectly distributing the square root over addition instead of multiplication.
