Math Problem Statement

Can you simplify this math equation

Can you simplify this math equation?

Solution

To simplify 300\sqrt{300}, let's break down the number 300 into its prime factors and identify any perfect squares.

  1. First, factorize 300: 300=22×3×52300 = 2^2 \times 3 \times 5^2

  2. Now, we can express 300\sqrt{300} as: 300=22×3×52\sqrt{300} = \sqrt{2^2 \times 3 \times 5^2}

  3. Extract the perfect squares (222^2 and 525^2) from under the square root: 300=(2×5)2×3=103\sqrt{300} = \sqrt{(2 \times 5)^2 \times 3} = 10\sqrt{3}

So, the simplified form of 300\sqrt{300} is: 10310\sqrt{3}

Would you like further details or have any questions?

Here are some related questions to deepen your understanding:

  1. How do we find the prime factors of a number?
  2. What other methods can be used to simplify square roots?
  3. Why can perfect squares be factored out of a square root?
  4. How would you simplify 450\sqrt{450} in a similar way?
  5. What are some practical applications of simplifying square roots?

Tip: Always look for perfect squares within a number when simplifying square roots, as this can often help simplify the expression.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Prime Factorization
Simplifying Expressions

Formulas

√(a^2 * b) = a√b

Theorems

Product of Square Roots

Suitable Grade Level

Grades 8-10