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

2 Answers
Apr 24, 2017

Answer:

25

Explanation:

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

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

#sqrt625 = +-25#

Apr 24, 2017

Answer:

#sqrt(625)=+-25#

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

Explanation:

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#