Math Problem Statement

Express in simplest radical form. square root of, 27, end square root 27

Solution

The square root of 27 can be simplified by factoring 27 into its prime factors.

27=33=32×3\sqrt{27} = \sqrt{3^3} = \sqrt{3^2 \times 3}

Now, you can take the square root of 323^2 (which is 9) out of the radical:

27=33\sqrt{27} = 3\sqrt{3}

So, the simplest radical form of 27\sqrt{27} is 333\sqrt{3}.

Would you like more details or have any other questions?

Here are 5 related questions:

  1. How would you simplify 72\sqrt{72}?
  2. What is the value of 12\sqrt{12} in simplest radical form?
  3. How do you simplify 50\sqrt{50}?
  4. Can you simplify 18\sqrt{18}?
  5. What is the simplified form of 75\sqrt{75}?

Tip: When simplifying square roots, look for perfect squares (like 4, 9, 16, etc.) within the number to factor out.

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Math Problem Analysis

Mathematical Concepts

Radicals
Simplifying Square Roots
Prime Factorization

Formulas

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

Theorems

Fundamental Theorem of Arithmetic
Properties of Square Roots

Suitable Grade Level

Grades 6-8