Video Transcript
What is the square root of negative 25?
In order to answer this question, we will use our knowledge of imaginary numbers as well as the laws of radicals or surds. The square root of negative one is equal to the imaginary number 𝑖. And the square root of 𝑎 multiplied by 𝑏 is equal to the square root of 𝑎 multiplied by the square root of 𝑏. As negative 25 is equal to 25 multiplied by negative one, we can write the square root of negative 25 as the square root of 25 multiplied by the square root of negative one. The square root of 25 is equal to five. And as already stated, the square root of negative one is equal to 𝑖. This means that the square root of negative 25 is equal to five 𝑖.