What is the square root of 464?

1 Answer
Oct 16, 2015

Answer:

#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)#