How do you simplify #sqrt392#?

1 Answer
Aug 18, 2016

Answer:

#14sqrt(2)#

Explanation:

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#