We are asked to determine the square root of 176. This number is not a perfect square, which means there is no natural number such that the product by itself is 176. We can simplify this radical as following:
![\sqrt[]{176}](https://img.qammunity.org/2023/formulas/mathematics/college/umq4wpd2n0wmkqs03folwlr605ymwkm4er.png)
We know that

We replace that in the radical:
![\sqrt[]{176}=\sqrt[]{16*11}](https://img.qammunity.org/2023/formulas/mathematics/college/zxvkklf95jjl2510d3en5c0ud8ygdqjihw.png)
Now we use the following property:
![undefined]()