How do you solve #(\sqrt{15})^{2}+(\sqrt{65})^{2}=x^{2}#?

1 Answer
smendyka
Dec 4, 2017

See a solution process below:

Explanation:

First, square the two terms on the left side of the equation and then add the results together. Remember:

#(sqrt(x))^2 = x#

#(sqrt(15))^2 + (sqrt(65))^2 = x^2#

#15 + 65 = x^2#

#80 = x^2#

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

#sqrt(80) = sqrt(x^2)#

#+-sqrt(16 * 5) = x#

#+-sqrt(16)sqrt(5) = x#

#+-4sqrt(5) = x#

#x = +-4sqrt(5)#

Or

#x = +-8.94# rounded to the nearest hundredth.

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