Math Problem Statement

Express in simplest radical form: √(9x^12).

Solution

Let's solve the given problem.

We are tasked with simplifying the radical expression:

9x12\sqrt{9x^{12}}

Step-by-step Solution:

  1. Separate the square root: 9x12=9x12\sqrt{9x^{12}} = \sqrt{9} \cdot \sqrt{x^{12}}

  2. Simplify each term:

    • The square root of 99 is 33: 9=3\sqrt{9} = 3
    • The square root of x12x^{12} is x6x^6 (since x12=x12/2=x6\sqrt{x^{12}} = x^{12/2} = x^6).
  3. Combine the results: 9x12=3x6\sqrt{9x^{12}} = 3x^6

Final Answer:

3x6\boxed{3x^6}

This matches the first option in the provided answers.


Do you want further clarification or more examples?

Here are 5 related questions to expand your understanding:

  1. How do you simplify 16x8\sqrt{16x^8}?
  2. What is the general rule for simplifying a2b2n\sqrt{a^2b^{2n}}?
  3. How do fractional exponents relate to square roots?
  4. How do you handle expressions like 25x11\sqrt{25x^{11}}, where the exponent is odd?
  5. What are the properties of square roots and exponents used in this problem?

Tip: When simplifying square roots, always factor out perfect squares to simplify the process!

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Math Problem Analysis

Mathematical Concepts

Simplification of square roots
Radicals
Exponents

Formulas

√(ab) = √a × √b
√(x^n) = x^(n/2)

Theorems

Properties of square roots and exponents

Suitable Grade Level

Grades 8-10