What is the #sqrt145# in simplest radical form?

2 Answers
Dec 19, 2017

#\sqrt{145}=\sqrt{5*29}#

5 and 29 are both prime numbers , so the simplest form of #\sqrt{145}# is #\sqrt{145}#

Dec 19, 2017

Answer:

Simplest form = #sqrt(145) #

#approx 12.042 #

Explanation:

We must recall our laws of radicals:

#sqrt(a*b*c) = sqrt(a)*sqrt(b)*sqrt(c) #

So the next thing to do is to find the prime factors of #145#

#145 = 5 * 29 #

#=> sqrt(145) = sqrt(5)*sqrt(29) #

But we see #sqrt(5) # and #sqrt(29) # are both in the simplest form as they are both prime, cant be factored any more

Hence #sqrt(145) # is in its simplest form already

#sqrt(145) approx 12.042 #