Math Problem Statement

√4 + √25 - √9 - √2² × √7² + 4

Solution

The expression in the image is:

4+25922×72+4\sqrt{4} + \sqrt{25} - \sqrt{9} - \sqrt{2^2} \times \sqrt{7^2} + 4

Let's break it down step by step:

  1. 4=2\sqrt{4} = 2
  2. 25=5\sqrt{25} = 5
  3. 9=3\sqrt{9} = 3
  4. 22=2\sqrt{2^2} = 2
  5. 72=7\sqrt{7^2} = 7

Now, substitute these values back into the expression:

2+53(2×7)+42 + 5 - 3 - (2 \times 7) + 4

Simplify:

2+5314+42 + 5 - 3 - 14 + 4

Now, perform the operations from left to right:

(2+5)=7(2 + 5) = 7 73=47 - 3 = 4 414=104 - 14 = -10 10+4=6-10 + 4 = -6

The final result is:

6\boxed{-6}

Would you like a further breakdown or explanation of any step?

Here are five related questions to expand your understanding:

  1. What is the general rule for simplifying square roots of perfect squares?
  2. How does the order of operations affect the calculation in this expression?
  3. Why is 22\sqrt{2^2} simplified to 2, and how does this rule apply to other squares?
  4. How does multiplication inside square roots differ from operations outside them?
  5. Can square roots of non-perfect squares be simplified similarly?

Tip: Always resolve powers and square roots before applying addition, subtraction, or multiplication.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Order of Operations
Basic Arithmetic

Formulas

√x where x is a perfect square

Theorems

Order of Operations (PEMDAS)

Suitable Grade Level

Grades 6-8