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 a=2a = 2 and b=22b = 2\sqrt{2}, we can use the Pythagorean theorem to find the hypotenuse cc of a right triangle with sides aa and bb.

The Pythagorean theorem states:

c=a2+b2c = \sqrt{a^2 + b^2}

Substitute the values of aa and bb into the formula:

c=22+(22)2c = \sqrt{2^2 + (2\sqrt{2})^2}

Now, calculate each term inside the square root:

  1. 22=42^2 = 4
  2. (22)2=22(2)2=42=8(2\sqrt{2})^2 = 2^2 \cdot (\sqrt{2})^2 = 4 \cdot 2 = 8

Add these results together:

c=4+8c = \sqrt{4 + 8}

c=12c = \sqrt{12}

The square root of 12 can be simplified further:

c=4×3=4×3=23c = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}

So, the length of the hypotenuse cc is 232\sqrt{3}.

Summary

Given a=2a = 2 and b=22b = 2\sqrt{2}, using the Pythagorean theorem, the result for the hypotenuse cc is 232\sqrt{3}.

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Related Questions

  1. What is the Pythagorean theorem, and how is it derived?
  2. How do you simplify square roots like 12\sqrt{12}?
  3. What are the properties of right triangles in relation to the Pythagorean theorem?
  4. Can you explain the process of squaring numbers involving square roots?
  5. 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