Math Problem Statement

Express in simplest radical form: √12

Solution

To express 12\sqrt{12} in its simplest radical form:

  1. Begin by finding the prime factorization of 12: 12=22×312 = 2^2 \times 3
  2. Now break down 12\sqrt{12} using these factors: 12=22×3\sqrt{12} = \sqrt{2^2 \times 3}
  3. Since 222^2 is a perfect square, you can take 2 out of the square root: 12=23\sqrt{12} = 2\sqrt{3}

Thus, the simplest radical form of 12\sqrt{12} is 232\sqrt{3}.

Would you like more details on this, or do you have any questions?

Here are 5 related questions:

  1. How would you simplify 18\sqrt{18}?
  2. What is the simplest radical form of 50\sqrt{50}?
  3. How do you simplify 75\sqrt{75}?
  4. Can you simplify 8\sqrt{8} using the same method?
  5. What is the value of 232\sqrt{3} to two decimal places?

Tip: When simplifying square roots, always look for the largest perfect square factor.

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Math Problem Analysis

Mathematical Concepts

Simplifying Radicals
Square Roots
Prime Factorization

Formulas

√(a × b) = √a × √b

Theorems

Properties of Square Roots

Suitable Grade Level

Grades 6-8