How do you simplify $sqrt392$ ?

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Answer 1 · 2016-08-18T07:25:47

$14sqrt(2)$

When simplifying roots of Natural numbers it is often useful to express the number as the product of prime numbers.

Note: $392 = 2xx2xx2xx7xx7$

Therefore: $sqrt(392) = sqrt(2xx2xx2xx7xx7)$

For every pair of prime factors can then be taken through the $sqrt$ as follows:

$sqrt(392) = 2xx7xxsqrt(2)$

$sqrt(392) = 14sqrt2$

How do you simplify sqrt392sqrt392?