Math Problem Statement

Simplify the square root of 50 (√50).

Solution

The problem shown in the image is to simplify the square root of 50, 50\sqrt{50}.

Here's the solution:

  1. Break down 50 into its prime factors:
    50=2×25=2×5250 = 2 \times 25 = 2 \times 5^2.

  2. Apply the square root:
    50=2×52\sqrt{50} = \sqrt{2 \times 5^2}.

  3. Simplify:
    50=52\sqrt{50} = 5\sqrt{2}.

Thus, the simplified form of 50\sqrt{50} is 525\sqrt{2}.

Would you like more details on the simplification? Here are five related questions:

  1. How do you simplify square roots of other numbers?
  2. What is the general method for simplifying square roots?
  3. Can the square root of 50 be simplified further?
  4. How do you approximate 2\sqrt{2} as a decimal?
  5. What are other common square root simplifications?

Tip: Always check for perfect square factors when simplifying square roots!

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Math Problem Analysis

Mathematical Concepts

Simplification of square roots
Prime factorization

Formulas

√(a × b) = √a × √b

Theorems

Square root simplification

Suitable Grade Level

Grades 7-9