# Define The Square Root Of A Product

## 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 = √4√9 = 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 = 8√3. 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.

## Combined As Products? |
## Math Expression |
## Answer |
---|---|---|

Yes | √192 | 8√3 |

Yes | 2√(5 × 3) | 2√15 |

Yes | √(9 × 16) | √9 × √16 = √9√16 = 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