Math Problem Statement
Solution
To solve the given expression, let's break it down step by step.
Problem:
Solution:
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Use the property of square roots:
Applying this property:
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Expand using the difference of squares formula: Here, and . Substituting these values:
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Simplify: So:
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Return to the square root:
Final Answer:
The result of the expression is:
Would you like further clarification or additional examples?
Here are 5 related questions for further exploration:
- How does the difference of squares formula simplify similar expressions?
- Can the square root of 13 be approximated to a decimal value?
- What happens if the product includes complex numbers?
- How would this problem change if a different term replaced ?
- What are other ways to simplify products of square roots?
Tip: Always look for the possibility of applying algebraic identities like the difference of squares when dealing with nested square root expressions!
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Math Problem Analysis
Mathematical Concepts
Square roots
Difference of squares
Formulas
√a · √b = √(a · b)
(a - b)(a + b) = a^2 - b^2
Theorems
Difference of squares formula
Suitable Grade Level
Grades 7-9
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