How do you solve #k^2=76#?

1 Answer
smendyka
Jul 4, 2017

See a solution process below:

Explanation:

First, take the square root of each side of the equation to solve for #k# while keeping the equation balanced. Remember, the square root of a number produces both a positive and negative result.

#sqrt(k^2) = +-sqrt(76)#

#k = +-sqrt(76)#

We can now simplify this using this rule for radicals:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#k = +-sqrt(color(red)(4) xx color(blue)(19))#

#k = +-sqrt(color(red)(4)) xx sqrt(color(blue)(19))#

#k = +-2 xx sqrt(color(blue)(19))#

#k = +-2sqrt(color(blue)(19))#

If necessary: #sqrt(19) = 4.359# rounded to the nearest thousandth

#k = +-2 * 4.359#

#k = +-8.718# rounded to the nearest thousandth

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