Textbook Question
Simplify each radical. Assume all variables represent positive real numbers. ⁶√√5³
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0. Review of Algebra
Simplifying Radical Expressions
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Simplify the radical.
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Verified step by step guidance1
Identify the expression to simplify: \( 75\sqrt{75} \).
Factor the number under the square root to find perfect squares: \( 75 = 25 \times 3 \).
Rewrite the expression using the factorization: \( 75\sqrt{75} = 75\sqrt{25 \times 3} \).
Apply the property of square roots: \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \). This gives \( 75\sqrt{25} \times \sqrt{3} \).
Simplify \( \sqrt{25} \) to 5, resulting in \( 75 \times 5 \times \sqrt{3} \).
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