Math Problem Statement

Simplify the expression: 2√30 * 3√2

Solution

The expression in the image is:

230322\sqrt{30} \cdot 3\sqrt{2}

We can simplify this step by step:

  1. Multiply the numerical coefficients: 23=62 \cdot 3 = 6

  2. Multiply the square roots: 302=302=60\sqrt{30} \cdot \sqrt{2} = \sqrt{30 \cdot 2} = \sqrt{60}

Thus, the expression becomes: 6606\sqrt{60}

Now, simplify 60\sqrt{60}: 60=415=215\sqrt{60} = \sqrt{4 \cdot 15} = 2\sqrt{15}

So, the entire expression simplifies to: 6215=12156 \cdot 2\sqrt{15} = 12\sqrt{15}

The simplified result is: 121512\sqrt{15}

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

  1. How do you multiply two square roots in general?
  2. What is the process of simplifying a square root like 60\sqrt{60}?
  3. How can you factor square roots more efficiently?
  4. What happens when you add or subtract square roots?
  5. How can this technique be applied to algebraic expressions involving roots?

Tip: When simplifying square roots, always check for perfect square factors (e.g., 4,9,164, 9, 16) to simplify the expression further.

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Math Problem Analysis

Mathematical Concepts

Simplification
Multiplication of Radicals

Formulas

√a * √b = √(a*b)
a√b * c√d = (a*c)√(b*d)

Theorems

Properties of Square Roots
Simplification of Radicals

Suitable Grade Level

Grades 8-10