What is the square root of 625 simplified in radical form?

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Answer 1 · 2017-04-24T04:07:56

25

#sqrt625 = sqrt (25*25) =sqrt (25^2)=25#

Also, let's not forget that -25 works too!

#sqrt625 = +-25#

Answer 2 · 2017-04-24T14:37:09

#sqrt(625)=+-25#

If no calculator to hand it is always worth trying this type of trick

Consider the last digit of 625

This is 5. So the first question is, what times itself give the last digit of 5.

Known that #5xx5=25# giving us the last digit so 5 is a #ul("potential")# part of the solution

Consider the hundreds ie 600

#10xx10=100<600#
#20xx20=2xx200=400<600#
#30xx30=3xx300=900>600 color(red)(" Fail as too large")#

Putting this together lets test #25xx25#

#=(20+5)xx25= 500+125=625# as required

However: #color(green)((+25)xx(+25))color(blue)(=(-25)xx(-25))color(magenta)( = + 625)#

So #sqrt(625)=+-25#
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#color(blue)("Additional comment")#

If all else fails and you do not have a calculator to hand build a prime factor tree.

Tony B

From this observe that we have #5^2xx5^2->25xx25#

So #sqrt(625)->sqrt(25^2)=+-25#