What is the square root of 164 simplified in radical form?

2 Answers
May 24, 2017

Answer:

#2sqrt(41)#

Explanation:

Step 1. Find all the factors of #164#
#164=2*82=2*2*41=2^2*41#

[#41# is a prime number]

Step 2. Evaluate the square root
#sqrt(164)=sqrt(2^2*41)=2sqrt(41)#

May 24, 2017

Answer:

#2sqrt41#

Explanation:

We can think of two numbers that multiply to #164#. If we divide #164# by #4# we get #41#. We can write an expression like this:

#sqrt(4)*sqrt(41)=sqrt(164)#

If we look closely, we can see that we have a #sqrt4# and so we can simplify it by saying #sqrt4=2#.

Rewriting the expression:

#2*sqrt41=sqrt164#

So the #sqrt164# can be simplified to #2sqrt41# in radical form.

The goal of these problems is to break down the radical using at least one perfect square (e.g #4,9,16,25,36,49#.etc) which is why I chose #4# because you can easily find the square root of #4#.