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Simplify √(125)×√(320)?
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Simplify √(125)×√(320)?
Simplifying √(125)×√(320)
Finding the prime factorization of 125
- 125 ÷ 5 = 25
- 25 ÷ 5 = 5
125 can be written as 5 × 5 × 5 or as 5³
Finding the prime factorization of 320
- 320 ÷ 2 = 160
- 160 ÷ 2 = 80
- 80 ÷ 2 = 40
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
320 can be written as 2⁶ × 5
Combining the square roots
√(125)×√(320) = √(5³) × √(2⁶ × 5)
Using the product rule of square roots, we can simplify the expression:
√(5³) × √(2⁶ × 5) = √(5³ × 2⁶ × 5)
Combining the factors inside the square root gives:
√(5³ × 2⁶ × 5) = √(2⁶ × 5⁴)
Using the product rule of exponents, we can simplify this expression further:
√(2⁶ × 5⁴) = √(2⁶) × √(5⁴)
Simplifying the square roots gives:
√(2⁶) × √(5⁴) = 2³ × 5² = 200
Final answer
√(125)×√(320) can be simplified to 200.
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Simplify √(125)×√(320)?
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Simplify √(125)×√(320)? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Simplify √(125)×√(320)? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify √(125)×√(320)?.
Simplify √(125)×√(320)? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Simplify √(125)×√(320)? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify √(125)×√(320)?.
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