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Math K-Plus

Define The Square Root Of A Product

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How Do We Compute The Square Root Of A Product


Before we move forward and learn about Square Root Of A Product, be sure you understand the basics. Recommended reading: Square Roots.
  • The root of a product is the product of the roots.
  • A real example of taking a square root of a product: √(4 × 9) = √4 × √9 = √49 = 2 × 3 = 6.
  • Another real example of taking a square root of a product: √192 = √(2 × 2 × 2 × 2 × 2 × 2 × 3) = 2 × 2 × 2 × √3 = 83. This is a fairly complex example. However, it can easily be solved by computing the Prime Factorization of 192.
  • There is no way to combine the square root sum of two numbers (like we can with products). You can simplify: √(3 + 2) = √5.
  • There is no way to combine the square root difference of two numbers (like we can with products). You can simplify: √(3 - 2) = √1 = 1.

Syntax Example

Combined As Products?


Math Expression


Answer


Yes 192 8√3
Yes 2√(5 × 3) 2√15
Yes (9 × 16) 9 × √16 = √916 = 3 × 4 = 12
No (5 + 4) 9 = 3
No (5 - 4) 1 = 1





Please Read! To use this calculator is easy. You can use any input format shown in the table above. You indicate the radical sign with the letter "r". Example 10r(7-3) = 10√(7-4) = 10√3


Product of Square Roots Calculator
Enter The Number Here Then Press The SUBMIT Button