Question

Write √-175 in simplest radical form.

Answer 1

5i√7

Step-by-step Step-by-step explanation:

To evaluate the value of √-175, we have to undersrand that in the set of all real numbers, evaluating negative numbers in the radical is not possible. This is because there are no numbers when squared and result in negative. Thus, in set of real numbers, there are no results that satisfy the question.

However, we can indeed find the value within the complex set. We define that:

`\displaystyle{i = √( - 1) }`

So we can separate two surds as:

`\displaystyle{ √(175) √( - 1) = √(175)i }`

Then simplify √175 normally:

`\displaystyle{ √(175)i = √(5 * 5 * 7) i} \\ \\ \displaystyle{ = 5 i√(7) }`

Hence, the simplified form is 5i√7