Math Problem Statement

Simplify the radical expression. StartRoot 12 EndRoot

Solution

To simplify the radical expression 12\sqrt{12}, we begin by factoring 12 into its prime factors:

12=4×312 = 4 \times 3

We know that 4=2\sqrt{4} = 2, so we can simplify 12\sqrt{12} as:

12=4×3=4×3=23\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}

Thus, the simplified form of 12\sqrt{12} is:

232\sqrt{3}

Would you like to go over the process in more detail, or do you have any other questions? Here are some related questions you might find useful:

  1. How do you simplify a square root with a larger number, like 72\sqrt{72}?
  2. Can all square roots be simplified?
  3. What is the difference between simplifying square roots and cube roots?
  4. How do you add or subtract square roots?
  5. What happens if the number inside the square root is a perfect square?

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

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Math Problem Analysis

Mathematical Concepts

Simplifying Square Roots
Prime Factorization

Formulas

\( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \)
\( \sqrt{4} = 2 \)

Theorems

Product property of square roots

Suitable Grade Level

Grades 6-8