What is Square Root 144?
Finding the square and square root of a number are inverse operations. To find the square of a number you need to multiply the number by itself.
For example: To find the square of a number 12, we will multiply the number by itself, that is, 12 × 12 = 144
Similarly, to find the square root of 144, we will do the inverse operation.
A square root is represented by the radical symbol:‘√’.
Since, \(12^2~=~144 \)
\(\Rightarrow \sqrt{144}~=~\sqrt{12^2}~=~12 \)
Deriving the Square Root with Prime Factorization
We will calculate the Square root of 144 by prime factorization method:
Step 1: Find the prime factors of 144
∴144 = 2 × 2 × 2 × 2 × 3 × 3
Step 2: Make pairs of identical factors.
144 = \((2~\times~2)~\times~(2~\times~2)~\times(3~\times~3) \)
Step 3: Take a factor from each pair and multiply them to get the square root.
\(\sqrt{144}~=~\sqrt{(2~\times~2)~\times~(2~\times~2)~\times(3~\times~3)} \)
\(\Rightarrow \sqrt{144}~=~2~\times~2~\times~3 \)
\(\Rightarrow \sqrt{144}~=~12 \)
So, the square root of 144 is 12.
Definition of Negative Square Roots
Each number has two square roots, one is positive and the other is negative with the same absolute value.
Let us understand this with example.
\(12~\times~12~=~144\)
\(-12~\times~-12~=~144\) [Since, \((-)~\times~(-)~=~(+)\)]
So the square of -12 is 144 and square of 12 is also 144, so we can say that square roots of 144 are 12 and -12 both.
\(\Rightarrow ~\sqrt{144}~=~\pm~12\)
In general,
Rapid Recall
Solved Square Root of 144 Examples
Example 1: The area of the circular table top is 452.16 square centimeters. Find the radius of the table top.
Solution:
\(A~=~\pi~r^2\) Write the formula for area of circle
\(452.16~=~3.14~\times~r^2\) Substitute 452.16 for A and 3.14 for \(\pi\).
\(144~=~r^2\) Divide by 3.14 on each side
\(\sqrt{144}~=~\sqrt{r^2}\) Take positive square root of each side
\(12~=r\) Simplify
So, the radius of the table top is 12 centimeters.
Example 2: Evaluate \(10~\sqrt{144}~\times~2~\sqrt{144}\)
Solution:
Given expression: \(10~\sqrt{144}~\times~2~\sqrt{144}\)
\(10~\sqrt{144}~\times~2~\sqrt{144}~=~(10~\times~12)~\times~(2~\times~12)\) [Substitute 12 for \(\sqrt{144}\) ]
\(=~120~\times~24\)
\(=~2880\)
Hence, the value of given expression \(10~\sqrt{144}~\times~2~\sqrt{144}\) is 2880.
Example 3: A square shaped board has an area of 144 square inches. Find the edge length of the board.
Solution: The board is square in shape, use the area of square formula to find edge length.
\(A~=~{side}^2\) Write the formula for area of square
\(144~=~{side}^2\) Substitute 144 for A
\(\sqrt{144}~=~\sqrt{{side}^2}\) Take positive square root of each side
\(12~=~side\) Simplify
So, the edge length of the board is 12 inches.
There are two square roots of 144 which are 12 and -12.
‘±’ stands for two results, one of which is positive and the other is negative with the same absolute value.
The square root of 144 is ±12 which are integers so 144 is a perfect square.
The square root of 144 in radical form is written as \(\sqrt{144}\).