Math Problem Statement
if it is known that a is 2 and b is 2 the square root of 2 then the result is (squared root)....... (using Pythagoras)
Solution
Given that and , we can use the Pythagorean theorem to find the hypotenuse of a right triangle with sides and .
The Pythagorean theorem states:
Substitute the values of and into the formula:
Now, calculate each term inside the square root:
Add these results together:
The square root of 12 can be simplified further:
So, the length of the hypotenuse is .
Summary
Given and , using the Pythagorean theorem, the result for the hypotenuse is .
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Related Questions
- What is the Pythagorean theorem, and how is it derived?
- How do you simplify square roots like ?
- What are the properties of right triangles in relation to the Pythagorean theorem?
- Can you explain the process of squaring numbers involving square roots?
- What are some real-world applications of the Pythagorean theorem?
Tip
When dealing with square roots, always look for ways to simplify by finding perfect squares within the radical.
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Math Problem Analysis
Mathematical Concepts
Pythagorean theorem
Square roots
Formulas
Pythagorean theorem: c = sqrt(a^2 + b^2)
Theorems
Pythagorean theorem
Suitable Grade Level
Grades 9-12
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