Math Problem Statement

Simplify √18

Solution

The expression you need to simplify is 18\sqrt{18}. Let's break it down.

We can express 1818 as a product of perfect squares:

18=9×2=9×2=32\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}

So, 18\sqrt{18} simplifies to:

323\sqrt{2}

Would you like a further explanation on the steps? Here are some related questions:

  1. How do you simplify other square roots involving non-perfect squares?
  2. What is the difference between simplifying 18\sqrt{18} and estimating its decimal value?
  3. Can all square roots be simplified in this way?
  4. What are examples of other square roots that simplify similarly to 18\sqrt{18}?
  5. How can simplifying square roots help in solving larger algebraic problems?

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

Square Root Theorem

Suitable Grade Level

Grades 7-10