Example 1

a) Calculate the length of one side of a square floor when the floor area is [[$ 25 $]] m [[$ ^ 2 $]].

Solution:

The area of the square is [[$ 25 $]] m [[$ ^ 2 $]], so the length of one side must be [[$ 5 $]] m. This is the case because [[$ 5 $]] m · [[$ 5 $]] m [[$ = 25 $]] m [[$ ^ 2 $]].


b) What if the area of the square floor is [[$ 20 $]] m [[$ ^ 2 $]]. What is the length of one side then?

Solution:

If the side length was [[$ 4 $]] m, the floor area would be [[$ 4 $]] m · [[$ 4 $]] m [[$ = 16 $]] m [[$ ^ 2 $]]. The side length is now not an integer, but must be between [[$ 4 $]] m and [[$ 5 $]] m.

The problem could be solved by experimentation, but the solution is easier to find by taking the square root of [[$ 20 $]] with a calculator.

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The marking is read as "the square root of 20".

The value of the square root can be calculated by typing the radical sign and 20 to a calculator. 

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The answer can be checked as follows: ([[$ 4.47 $]]​m)[[$ ^2 $]]​ [[$ = 19.9809 $]]​ m[[$ ^2 ≈ 20 $]]​ m[[$ ^2 $]]​.

Taking the square root of a number is the inverse function of raising the number to a square. The square root thus answers the question, “Which number must be raised to another power to obtain the number in question?”. A square root cannot be taken from a negative number, and the value of a square root is never negative.

Example 2

a) The square root of number [[$ 16 $]] is [[$ \sqrt{16} = 4 $]], because the square of [[$ 4 $]] is [[$ 4^2=16 $]] .

b) The square root of the number [[$ 9 $]] [[$ \sqrt{9} = 3 $]], because the square of the number [[$ 3 $]] is [[$ 3 ^ 2 = 9 $]] .

Example 3