What is the square root of 156.25?

1 Answer
Sep 18, 2015

Answer:

#sqrt(156.25) = 25/2#

Explanation:

#15625 = 5^6#

So #156.25 = (5^6)/100 = (5^6)/(2^2*5^2) = 5^4/2^2#

If #a, b >= 0#, then #sqrt(a/b) = sqrt(a)/sqrt(b)#

If #a, b, c > 0# then #a^(bc) = (a^b)^c#

So #sqrt(156.25) = sqrt(5^4/2^2) = sqrt(5^4)/sqrt(2^2) = sqrt((5^2)^2)/sqrt(2^2) = 5^2/2 = 25/2#