Question

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

Answer 1

25

Explanation:

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

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

`sqrt625 = +-25`

Answer 2

`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`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Additional comment")`

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

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

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