Math Problem Statement

Fully simplify √48

Solution

To fully simplify 48\sqrt{48}, we proceed as follows:

  1. Factorize 48 into its prime factors:
    48=16×348 = 16 \times 3
    Recognizing that 16 is a perfect square, we can rewrite:
    48=16×3\sqrt{48} = \sqrt{16 \times 3}

  2. Use the square root property:
    The property a×b=a×b\sqrt{a \times b} = \sqrt{a} \times \sqrt{b} allows us to split the square root:
    48=16×3\sqrt{48} = \sqrt{16} \times \sqrt{3}

  3. Simplify:
    Since 16=4\sqrt{16} = 4, we get:
    48=43\sqrt{48} = 4\sqrt{3}

Final Answer:

43\boxed{4\sqrt{3}}

Would you like me to explain any step further? Let me know if you need more clarification!


Related Questions:

  1. How do you simplify 72\sqrt{72}?
  2. What are the steps to simplify 75\sqrt{75}?
  3. Can you explain how to identify perfect squares within a number?
  4. Simplify 108\sqrt{108} and explain your method.
  5. What is the square root of 48 rounded to 2 decimal places?

Tip: Always look for the largest perfect square factor of a number when simplifying square roots.

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Math Problem Analysis

Mathematical Concepts

Simplifying Square Roots
Prime Factorization

Formulas

√(a × b) = √a × √b

Theorems

Properties of Square Roots

Suitable Grade Level

Grades 6-8