How do you simplify $\sqrt{392}$ $sqrt392$ ?

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Answer 1 · 2016-08-18T07:25:47

$14 \sqrt{2}$ $14sqrt(2)$

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

Note: $392 = 2 \times 2 \times 2 \times 7 \times 7$ $392 = 2xx2xx2xx7xx7$

Therefore: $\sqrt{392} = \sqrt{2 \times 2 \times 2 \times 7 \times 7}$ $sqrt(392) = sqrt(2xx2xx2xx7xx7)$

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

$\sqrt{392} = 2 \times 7 \times \sqrt{2}$ $sqrt(392) = 2xx7xxsqrt(2)$

$\sqrt{392} = 14 \sqrt{2}$ $sqrt(392) = 14sqrt2$

How do you simplify sqrt392√392sqrt392?