Math  /  Algebra

QuestionKuta Software - Infinite Algebra 1 Simplifying Radical Expressions Simplify. 1) 125n\sqrt{125 n}

Studdy Solution

STEP 1

1. We are asked to simplify the radical expression 125n\sqrt{125n}.
2. The expression involves a square root, which can be simplified by factoring out perfect squares.

STEP 2

1. Factor the number inside the square root into its prime factors.
2. Identify and extract perfect squares from the radical.
3. Simplify the expression by moving the perfect squares outside the square root.

STEP 3

Factor 125125 into its prime factors:
125=5×5×5=53 125 = 5 \times 5 \times 5 = 5^3

STEP 4

Identify perfect squares in the factorization of 125125. Notice that 525^2 is a perfect square.
125n=52×5×n \sqrt{125n} = \sqrt{5^2 \times 5 \times n}

STEP 5

Extract the perfect square 525^2 from the square root:
52×5×n=55n \sqrt{5^2 \times 5 \times n} = 5 \sqrt{5n}
The simplified form of the expression is:
55n \boxed{5 \sqrt{5n}}

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