Answer: [tex]\sqrt[3]{7}[/tex]
Step-by-step explanation: To simplify the square root of 63, let’s first start by setting up a factor tree. A factor tree is very useful when finding the prime factorization of a number and can help us see it visually. Once we make our factor tree, we need to find out what two numbers multiplied together will give us a product of 63.
In this case, 9 multiplied by 7 will give us a product of 63 so we can write both 9 and 7 under 63.
Next, we can factor 9 because 7 cannot be factored other than itself and 1. The number 9 factors into 3 and 3 so we can write these numbers under 9. Now that we found the factors, we are done with our factor tree. Notice that we have two pairs of 3’s in our factor tree so a 3 can come outside of the radical.
Also, there is a 7 in our factor tree which does not pair up so it can stay inside of the radical. Therefore, the answer to this problem is [tex]\sqrt[3]{7}[/tex].
