Math Problem Statement

simplify square rot of 320

Solution

To simplify 320\sqrt{320}, follow these steps:

  1. Factorize 320: 320=26×5320 = 2^6 \times 5

  2. Use the square root property: 320=26×5=26×5\sqrt{320} = \sqrt{2^6 \times 5} = \sqrt{2^6} \times \sqrt{5}

  3. Simplify 26\sqrt{2^6}: Since 26=(23)22^6 = (2^3)^2, we have: 26=23=8\sqrt{2^6} = 2^3 = 8

  4. Combine the results: 320=8×5\sqrt{320} = 8 \times \sqrt{5}

Final Answer:

320=85\sqrt{320} = 8\sqrt{5}

Would you like more explanation or examples related to this topic?


Related Questions:

  1. How do you simplify the square root of other composite numbers?
  2. What is the process to find the square root of a number that isn't a perfect square?
  3. How do you rationalize square root denominators?
  4. How is prime factorization used in simplifying radicals?
  5. What are the rules for multiplying and dividing square roots?

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

Square Roots
Simplification of Radicals
Prime Factorization

Formulas

√(a × b) = √a × √b
√(x^2) = x

Theorems

Properties of Square Roots
Fundamental Theorem of Arithmetic (Prime Factorization)

Suitable Grade Level

Grades 8-10