Question

Using prime factorization method, find the square root of the following:
(i) $390625$ (ii) $119025$ (iii) $193600$

Answer 1

(i) $390625$ can be factorized as

$\sqrt{5\times 5\times 5\times 5\times 5\times 5\times 5\times 5}$

$=5\times 5\times \times 5\times 5$

$=625$

(ii) $119025$ can be factorized as

$\sqrt{5\times 5\times 3\times 3\times 23\times 23}$

$=5\times 3\times 23$

$=345$

(iii) $193600$ can be factorized as

$\sqrt{5\times 5\times 2\times 2\times 2\times 2\times 2\times 2\times 11\times 11}$

$=5\times 2\times 2\times 2\times 11$

$=440$