Math Problem Statement

Wrote in simplest radical form

Simplify the expression √(18x^3y^6) into its simplest radical form.

Solution

The expression you provided is:

18x3y6\sqrt{18x^3y^6}

Let's simplify this expression into its simplest radical form.

Step 1: Prime factorization of the numerical part

First, factorize 18:

18=2×3218 = 2 \times 3^2

Step 2: Rewrite the square root expression

We can express the square root as:

18x3y6=2×32×x3×y6\sqrt{18x^3y^6} = \sqrt{2 \times 3^2 \times x^3 \times y^6}

Step 3: Simplify inside the square root

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Math Problem Analysis

Mathematical Concepts

Algebra
Radical Expressions
Prime Factorization

Formulas

√(a * b) = √a * √b
√(x^n) = x^(n/2)

Theorems

Simplification of Radicals

Suitable Grade Level

Grades 8-10