Math Problem Statement

What's the value of the equation in the image

Solution

To evaluate the expression provided in the image:

122\frac{1 - \sqrt{2}}{2}

We can approximate 2\sqrt{2} to 1.414. So, we get:

11.4142=0.4142=0.207\frac{1 - 1.414}{2} = \frac{-0.414}{2} = -0.207

Thus, the approximate value of 122\frac{1 - \sqrt{2}}{2} is 0.207-0.207.

Would you like more details or have any questions?

Here are some questions you might want to explore next:

  1. How do you rationalize the denominator of an expression like this?
  2. What are some properties of square roots that are useful in algebra?
  3. Can you show the exact value calculation instead of approximation?
  4. How can we use such expressions in solving real-world problems?
  5. What are the applications of irrational numbers in mathematics?

Tip: When working with square roots, it's often helpful to leave your answers in exact form unless an approximation is specifically required. This maintains precision in your calculations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Square Roots

Formulas

Quadratic formula

Theorems

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Suitable Grade Level

High School