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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

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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

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