Question

What is the square root of 464?

Answer 1

`4sqrt(29)`

Explanation:

This square root isn't the square root of a perfect square. The only thing we can do is to simplify the expression. First let's try dividing by two until we can't anymore:
`sqrt(464)=sqrt(2*232)=sqrt(2*2*116)=sqrt(2*2*2*58)=sqrt(2*2*2*2*29)=sqrt(16*29)`

At this point, we can't divide `29` anymore, because it is a prime number. You can split this expression in:
`sqrt(16)*sqrt(29) = 4sqrt(29)`