Math Problem Statement

Express in simplest radical for: √54

Solution

To simplify 54\sqrt{54}, follow these steps:

  1. Find the prime factors of 54: 54=2×3354 = 2 \times 3^3

  2. Group the prime factors: 54=2×32×3\sqrt{54} = \sqrt{2 \times 3^2 \times 3}

  3. Take the square root of the perfect square (which is 323^2): 54=32×6=36\sqrt{54} = \sqrt{3^2 \times 6} = 3\sqrt{6}

Thus, the simplified form of 54\sqrt{54} is: 363\sqrt{6}

Would you like a more detailed explanation or have any questions?


Here are some related questions you might find interesting:

  1. How would you simplify 72\sqrt{72}?
  2. Can you simplify 75\sqrt{75}?
  3. What is the value of 48\sqrt{48} in simplest radical form?
  4. How do you simplify 98\sqrt{98}?
  5. Can you simplify 200\sqrt{200}?

Tip: To simplify a square root, always look for the largest perfect square that divides the number under the root.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Radicals
Square Roots
Prime Factorization

Formulas

√a * √b = √(a * b)
Square root of a perfect square: √(n^2) = n

Theorems

Simplification of square roots
Prime factorization method for radicals

Suitable Grade Level

Grades 8-10