What is Square root of 464 in simplest radical form?

2 Answers
Fir3hawk
May 20, 2017

#4sqrt(29)#

Explanation:

First, we look for any perfect squares that could be a factor of #sqrt(464)# by finding factors of 464 that divide in evenly.

#464/4 = 116#
#464/9 = 51.5555#
#464/16 = 29#

It seems that 16 will be our highest factor, as it results in an answer of a prime #.

Now, we rework the equation as so:

#sqrt(464)# = #sqrt(16*29)# = #sqrt(16)*sqrt(29)#

Which simplifies into:

#sqrt(16)*sqrt(29)# = #4*sqrt(29)# = #4sqrt(29)#

Final answer: #4sqrt(29)#

EZ as pi
May 20, 2017

#4sqrt29#

Explanation:

For questions dealing with factors, roots, HCF and LCM of numbers, a good starting point is to write the number(s) as the product of the prime factors:

#464 = 2xx2xx2xx2 xx29#

Now we know what we are working with!

#sqrt464 = sqrt(2^4 xx29)" "larr# (index of 2 is even, #div2#)

#= 2^2sqrt29#

#=4sqrt29#

#29# is a prime number, so we leave it as #sqrt29#, nothing can be done there!

Related questions
See all questions in Simplification of Radical Expressions
Impact of this question
11385 views around the world
You can reuse this answer
Creative Commons License