Math Problem Statement

(√4 + √5 - √5)^2

Solution

The mathematical expression in the uploaded image is:

(4+55)2(\sqrt{4} + \sqrt{5} - \sqrt{5})^2

Step-by-Step Solution:

  1. Simplify inside the parentheses: 4+55\sqrt{4} + \sqrt{5} - \sqrt{5} Since 55=0\sqrt{5} - \sqrt{5} = 0, the expression simplifies to: 4\sqrt{4}

  2. Evaluate 4\sqrt{4}: 4=2\sqrt{4} = 2

  3. Square the result: (2)2=4(2)^2 = 4

Final Answer:

44

Would you like a detailed explanation of any specific step? Here are some related questions you might explore:


  1. What is the general rule for simplifying expressions involving square roots?
  2. How do we expand and simplify squared binomials like (a+b)2(a + b)^2?
  3. Why does aa\sqrt{a} - \sqrt{a} equal 0 for any value of aa?
  4. Can all square roots be simplified to whole numbers?
  5. What are some common mistakes to watch out for when simplifying square root expressions?

Tip: Always simplify expressions inside parentheses first before applying other operations!

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Math Problem Analysis

Mathematical Concepts

Simplification of Expressions
Square Roots
Exponents

Formulas

Simplify square roots
Simplify expressions within parentheses
Exponentiation rules

Theorems

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Suitable Grade Level

Grades 6-8