Math Problem Statement

Express in radical form square root 200

Solution

To express 200\sqrt{200} in its simplest radical form, follow these steps:

  1. Factor the number under the square root: 200=23×52200 = 2^3 \times 5^2

  2. Group the perfect squares: 200=(22×52)×2200 = (2^2 \times 5^2) \times 2

  3. Take the square root of the perfect squares: 200=(22×52)×2=2×5×2=102\sqrt{200} = \sqrt{(2^2 \times 5^2) \times 2} = 2 \times 5 \times \sqrt{2} = 10\sqrt{2}

Thus, the simplest radical form of 200\sqrt{200} is: 102\boxed{10\sqrt{2}}

Would you like more details on how to simplify radicals or ask any other questions?

Here are 5 related questions:

  1. How do you simplify 72\sqrt{72} in radical form?
  2. Can you simplify 50\sqrt{50} using the same method?
  3. What are perfect squares and why do they help in simplifying square roots?
  4. How can you simplify cube roots, such as 543\sqrt[3]{54}?
  5. How do you simplify higher degree roots like 324\sqrt[4]{32}?

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

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Math Problem Analysis

Mathematical Concepts

Radical Expressions
Simplifying Square Roots
Factorization

Formulas

\( \sqrt{a} = \sqrt{(b^2) \times c} = b\sqrt{c} \)

Theorems

Properties of Square Roots
Factorization of Numbers

Suitable Grade Level

Grades 6-8