Math Problem Statement

Express in simplest radical form. √50

Solution

The image you uploaded contains a mathematical problem asking to simplify the square root of 50.

Let's break this down.

We are asked to express √50 in its simplest radical form. Here's how you can do that:

  1. Factor 50 into prime factors:
    50=25×250 = 25 \times 2

  2. Simplify the square root:
    Since 2525 is a perfect square (25=5\sqrt{25} = 5), you can simplify the square root as follows: 50=25×2=25×2=52\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}

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

Would you like further clarification on this or any other related questions? Here are a few suggestions for more topics:

  1. What is the process for simplifying square roots with larger numbers?
  2. How do you simplify square roots of expressions with variables?
  3. Can you simplify cube roots in a similar way to square roots?
  4. What is the difference between rationalizing the denominator and simplifying radicals?
  5. How do you apply the Pythagorean Theorem when working with radicals?

Tip: Always look for perfect squares or cubes when simplifying radicals, as they can make the process easier and help in reducing the expression to its simplest form.

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Math Problem Analysis

Mathematical Concepts

Simplifying Radicals
Square Roots
Prime Factorization

Formulas

√a × √b = √(a × b)
√(a × b) = √a × √b

Theorems

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Suitable Grade Level

Grades 6-8