How do you simplify #sqrt(1008)#?

2 Answers

Answer:

#12sqrt7#

Explanation:

The largest perfect root you could pull would be #144# (#12^2#)

#1008/144= 7#

Apr 3, 2018

Answer:

The simplified radical is #12sqrt7#.

Explanation:

Simplifying radicals usually uses this rule:

#color(white)=sqrt(color(red)(a^2)color(blue)b)=sqrtcolor(red)(a^2)*sqrtcolor(blue)b=color(red)asqrtcolor(blue)b#

First, write out the factor pairs of #1008#. You can use a calculator or do it by hand, though the latter may take a while. Here they are:

https://www.calculatorsoup.com/calculators/math/factors.php

Now, look for the biggest square number in the factor pairs.

We can see that the square numbers present are #9#, #16#, #36#, but the biggest one is #144#. Now, split up #1008# into #144# and its factor pair, #7#, then use the above rule to simplify the radical:

#color(white)=sqrt(1008)#

#=sqrt(color(red)144*color(blue)7)#

#=sqrtcolor(red)144*sqrtcolor(blue)7#

#=sqrtcolor(red)(12^2)*sqrtcolor(blue)7#

#=color(red)12*sqrtcolor(blue)7#

#=color(red)12sqrtcolor(blue)7#

That's the simplified radical. You can use a calculator to check your work:

https://www.desmos.com/calculator

Hope this helped!