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 $sqrt(54)$ :

$7/1 = 7.0$

$103/14 ~~ 7.36$

$21193/2884 ~~ 7.34847$

$898285873/122241224 ~~ 7.34846922835$