Math Problem Statement

Express in simplest radical form. square root of, 45, end square root 45

Solution

To express 45\sqrt{45} in its simplest radical form, we can start by factoring 45.

45=9×545 = 9 \times 5

Now, take the square root of 9 since it is a perfect square:

45=9×5=9×5=35\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}

Thus, the simplest radical form of 45\sqrt{45} is:

353\sqrt{5}

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

Here are 5 related questions for further practice:

  1. Simplify 75\sqrt{75}.
  2. Simplify 50\sqrt{50}.
  3. Simplify 18\sqrt{18}.
  4. Simplify 80\sqrt{80}.
  5. Simplify 72\sqrt{72}.

Tip: Always look for perfect squares when simplifying square roots to make the process easier!

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Math Problem Analysis

Mathematical Concepts

Radical Expressions
Square Roots
Simplifying Radicals

Formulas

√(a * b) = √a * √b

Theorems

Properties of Square Roots

Suitable Grade Level

Grades 6-8