Math Problem Statement
Approximate using perfect squares. What is the square root of 78?
Solution
This worksheet asks to approximate the square root of 78 using perfect squares.
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First, note that is between two perfect squares: Therefore, .
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Since , the square root of 78 lies between and , which simplifies to:
The conclusion is:
Would you like a more detailed explanation or additional assistance on this?
Here are 5 related questions to further explore this topic:
- How can you estimate more precisely using interpolation?
- What is the decimal approximation of ?
- How do you determine the square roots of non-perfect squares?
- Why does fall between 8 and 9 specifically?
- How can you find the square root of any number using long division?
Tip: To improve your estimation of square roots, consider using decimal approximations and methods like interpolation between perfect squares.
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Math Problem Analysis
Mathematical Concepts
Number Sense
Square Roots
Estimation
Formulas
Square root approximation: if a < x < b, then √a < √x < √b
Theorems
Perfect square properties
Inequalities for square roots
Suitable Grade Level
Grades 6-8