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!

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