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

2 Answers
Apr 24, 2017

25

Explanation:

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

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

sqrt625 = +-25

Apr 24, 2017

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 BTony B

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

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