Math Problem Statement

√27•√3

Solution

To simplify the expression 273\sqrt{27} \cdot \sqrt{3}, we can use the property of square roots:

ab=ab\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}

Applying this to our problem:

273=273=81\sqrt{27} \cdot \sqrt{3} = \sqrt{27 \cdot 3} = \sqrt{81}

Now, since 81=9\sqrt{81} = 9, the simplified answer is:

99

Would you like a further breakdown of any step?


Here are some related questions:

  1. How do you simplify expressions with square roots?
  2. What are the properties of square roots for multiplication and division?
  3. How would you solve 455\sqrt{45} \cdot \sqrt{5}?
  4. Can you multiply square roots with different variables (like xy\sqrt{x} \cdot \sqrt{y})?
  5. How do you simplify the square root of a non-perfect square?

Tip: When multiplying square roots, try to simplify each square root separately before multiplying if possible—it can sometimes make the problem easier to solve.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Multiplication of Radicals

Formulas

√a • √b = √(a • b)

Theorems

Properties of Square Roots

Suitable Grade Level

Grades 7-9