# Math - Square Root - Word Problem

by Andrew
(Marikina City, Philippines)

Solve the following problems involving radicals.

The square root of the sum of a number and 12 is 5. Find the number.

### Comments for Math - Square Root - Word Problem

 Jan 15, 2012 Square Root - Word Problem by: Staff Question: by Andrew (Marikina City, Philippines) Solve the following problems involving radicals. The square root of the sum of a number and 12 is 5. Find the number. Answer: n = number Rewrite the problem statement as an equation: The square root of the sum of a number and 12 is 5 Eliminate the word “The” square root of the sum of a number and 12 is 5 replace the words “square root” with the √ symbol √ of the sum of a number and 12 is 5 Replace the words “sum of a number and 12” with n + 12 √ of n + 12 is 5 Eliminate the word “of”. Place parentheses around the “n + 12” √ (n + 12) is 5 Replace the word “is” with the = symbol √(n + 12) = 5 The equation which must be solved is: √(n + 12) = 5 Square each side of the equation [√(n + 12)]² = 5² [√(n + 12)] * [√(n + 12)] = 25 √[(n + 12) * √(n + 12)] = 25 √(n + 12)² = 25 n + 12 = 25 Subtract 12 from each side of the equation n + 12 - 12 = 25 - 12 n + 0 = 25 - 12 n = 13 >>>>> Final Answer: n = 13 Check the answer by substituting 13 for n in the original equation: √(n + 12) = 5 √(13 + 12) = 5 √(25) = 5 5 = 5, OK → n = 13 is a VALID solution Thanks for writing. Staff www.solving-math-problems.com