How do you find the square root of 54?

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Answer 1 · 2015-09-12T21:14:33

#sqrt(54) = 3sqrt(6) ~~ 7.34846922835#

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

#sqrt(54) = sqrt(3^2*6) = sqrt(3^2)sqrt(6) = 3sqrt(6)#

If you want an approximate value, then so long as you have memorised approximate values for #sqrt(2)# and #sqrt(3)# then it's just #3sqrt(2)sqrt(3)#

From memory:

#sqrt(2) ~~ 1.414213562373#
#sqrt(3) ~~ 1.73205080756#

Alternatively you could use a Newton Raphson type method, such as the one I describe in http://socratic.org/questions/how-do-you-find-the-square-root-28

If you started with #7#, this would give you successive rational approximations for #sqrt(54)#:

#7/1 = 7.0#

#103/14 ~~ 7.36#

#21193/2884 ~~ 7.34847#

#898285873/122241224 ~~ 7.34846922835#