Mastering SQRT() in Excel
Overview, Examples, and Assignments for Beginners
What is the SQRT() Function?
- The SQRT() function stands
for "square root."
- It returns the positive
square root of a given number.
- The square root of a number
xxx is a value yyy such that y×y=xy \times y = xy×y=x.
Syntax
SQRT(number)
- number: This is the number for
which you want to find the square root. It must be a non-negative number.
If you provide a negative number, Excel will return an error (#NUM!).
Examples
1. Basic Calculation:
o To find the square
root of 16:
=SQRT(16)
o Result: 4 (since 4×4=164
\times 4 = 164×4=16)
2. Using Cell
References:
o If you have a number
in cell A1 (let’s say 25), you can use:
=SQRT(A1)
o Result: 5 (since 5×5=255
\times 5 = 255×5=25)
3. Square Root of a
Non-Integer:
o To find the square
root of 20:
=SQRT(20)
o Result: Approximately 4.472
(since 4.472×4.472≈204.472 \times 4.472 \approx 204.472×4.472≈20)
Important Notes
- Negative Numbers: You cannot calculate the
square root of a negative number with SQRT(). For example, =SQRT(-1) will
result in an error.
- Zero: The square root of zero is
zero, so =SQRT(0) will return 0.
- Precision: The result may have
decimal places, depending on the number's value. You can use the ROUND()
function if you need to limit the number of decimal places.
Practical Applications
1. Finance: The square root is
often used in finance to calculate the volatility of investments.
2. Statistics: It is useful in
various statistical calculations, such as standard deviation.
3. Geometry: In geometry, it
helps in calculations involving areas and distances.
Example Scenario
Scenario: Calculating the Area of a Square
If you want to find the side length of a square given its area, you can
use the SQRT() function. For instance, if the area of a square is 64 square
units, you can find the length of one side using:
1. Area in Cell A1: Enter 64 in cell
A1.
2. Formula in Cell B1:
=SQRT(A1)
3. Result in Cell B1: 8 (since 8×8=648
\times 8 = 648×8=64)
Summary
- The SQRT() function is a
powerful and simple tool in Excel for finding square roots.
- Remember that it only works
with non-negative numbers.
- It has various applications
in finance, statistics, and geometry, making it a valuable function for
MBA students.
Assignments
Assignment 1: Basic Square Roots
Task: Calculate the square roots of the following numbers using the
SQRT() function:
1. 36
2. 49
3. 81
4. 100
Data Table:
|
Number |
Excel
Formula |
Expected
Result |
|
36 |
=SQRT(36) |
6 |
|
49 |
=SQRT(49) |
7 |
|
81 |
=SQRT(81) |
9 |
|
100 |
=SQRT(100) |
10 |
Solutions:
1. 36=6\sqrt{36} =
636=6
2. 49=7\sqrt{49} =
749=7
3. 81=9\sqrt{81} =
981=9
4. 100=10\sqrt{100} =
10100=10
Assignment 2: Using Cell References
Task: Use the numbers in cells A1 to A4 to find their square roots.
- A1: 25
- A2: 64
- A3: 144
- A4: 196
Data Table:
|
Cell |
Value |
Excel
Formula |
Expected
Result |
|
A1 |
25 |
=SQRT(A1) |
5 |
|
A2 |
64 |
=SQRT(A2) |
8 |
|
A3 |
144 |
=SQRT(A3) |
12 |
|
A4 |
196 |
=SQRT(A4) |
14 |
Solutions:
1. 25=5\sqrt{25} =
525=5
2. 64=8\sqrt{64} =
864=8
3. 144=12\sqrt{144} =
12144=12
4. 196=14\sqrt{196} =
14196=14
Assignment 3: Handling Errors
Task: What happens when you try to calculate the square root of negative
numbers? Test the following and note the result:
1. -1
2. -16
3. -36
Data Table:
|
Number |
Excel
Formula |
Expected
Result |
|
-1 |
=SQRT(-1) |
#NUM!
(Error) |
|
-16 |
=SQRT(-16) |
#NUM!
(Error) |
|
-36 |
=SQRT(-36) |
#NUM!
(Error) |
Solutions:
- All attempts to calculate
the square root of negative numbers return the error #NUM!, indicating
that the square root cannot be computed.
Assignment 4: Real-World Applications
Task: You are conducting a survey to determine the area of several
square plots of land in square meters. The areas of the plots are as follows:
1. Plot 1: 256 m²
2. Plot 2: 729 m²
3. Plot 3: 484 m²
4. Plot 4: 900 m²
Data Table:
|
Plot |
Area
(m²) |
Excel
Formula |
Expected
Result |
|
1 |
256 |
=SQRT(A2) |
16 |
|
2 |
729 |
=SQRT(A3) |
27 |
|
3 |
484 |
=SQRT(A4) |
22 |
|
4 |
900 |
=SQRT(A5) |
30 |
Solutions:
1. Plot 1:
256=16\sqrt{256} = 16256=16 (Side length = 16 m)
2. Plot 2:
729=27\sqrt{729} = 27729=27 (Side length = 27 m)
3. Plot 3:
484=22\sqrt{484} = 22484=22 (Side length = 22 m)
4. Plot 4:
900=30\sqrt{900} = 30900=30 (Side length = 30 m)
Assignment 5: Square Roots of Non-Integer Values
Task: Calculate the square roots of the following non-integer values
using the SQRT() function:
1. 10.24
2. 50.56
3. 200.25
4. 0.81
Data Table:
|
Value |
Excel
Formula |
Expected
Result |
|
10.24 |
=SQRT(A1) |
3.2 |
|
50.56 |
=SQRT(A2) |
7.1 |
|
200.25 |
=SQRT(A3) |
14.14 |
|
0.81 |
=SQRT(A4) |
0.9 |
Solutions:
1. 10.24≈3.2\sqrt{10.24}
\approx 3.210.24≈3.2
2. 50.56≈7.1\sqrt{50.56}
\approx 7.150.56≈7.1
3. 200.25≈14.14\sqrt{200.25}
\approx 14.14200.25≈14.14
4. 0.81=0.9\sqrt{0.81} =
0.90.81=0.9
Assignment 6: Combining with Other Functions
Task: Use the SQRT() function combined with ROUND() to round the square
roots of the following numbers to 2 decimal places:
1. 3.14
2. 8
3. 15.5
4. 50
Data Table:
|
Value |
Excel
Formula |
Expected
Result |
|
3.14 |
=ROUND(SQRT(A1),
2) |
1.77 |
|
8 |
=ROUND(SQRT(A2),
2) |
2.83 |
|
15.5 |
=ROUND(SQRT(A3),
2) |
3.94 |
|
50 |
=ROUND(SQRT(A4),
2) |
7.07 |
Solutions:
1. 3.14≈1.77\sqrt{3.14}
\approx 1.773.14≈1.77
2. 8≈2.83\sqrt{8}
\approx 2.838≈2.83
3. 15.5≈3.94\sqrt{15.5}
\approx 3.9415.5≈3.94
4. 50≈7.07\sqrt{50}
\approx 7.0750≈7.07
Assignment 7: Negative Values and Error Handling
Task: What happens when you try to calculate the square root of negative
numbers? Use the following negative numbers and observe the results:
1. -4
2. -64
3. -100
4. -225
Data Table:
|
Value |
Excel
Formula |
Expected
Result |
|
-4 |
=SQRT(A1) |
#NUM!
(Error) |
|
-64 |
=SQRT(A2) |
#NUM!
(Error) |
|
-100 |
=SQRT(A3) |
#NUM!
(Error) |
|
-225 |
=SQRT(A4) |
#NUM!
(Error) |
Solutions:
- All calculations of the
square root of negative numbers return the error #NUM!, indicating that
the square root cannot be computed for negative values.
Assignment 8: Area and Perimeter Calculations
Task: Given the area of various square fields, calculate both the side
length and the perimeter using the SQRT() function. The areas are:
1. 144 m²
2. 225 m²
3. 324 m²
4. 400 m²
Data Table:
|
Area
(m²) |
Excel
Formula for Side Length |
Excel
Formula for Perimeter |
Expected
Side Length |
Expected
Perimeter |
|
144 |
=SQRT(A1) |
=4*SQRT(A1) |
12 |
48 |
|
225 |
=SQRT(A2) |
=4*SQRT(A2) |
15 |
60 |
|
324 |
=SQRT(A3) |
=4*SQRT(A3) |
18 |
72 |
|
400 |
=SQRT(A4) |
=4*SQRT(A4) |
20 |
80 |
Solutions:
1. Area: 144 m²
o Side Length:
144=12\sqrt{144} = 12144=12 m
o Perimeter: 4×12=484
\times 12 = 484×12=48 m
2. Area: 225 m²
o Side Length:
225=15\sqrt{225} = 15225=15 m
o Perimeter: 4×15=604
\times 15 = 604×15=60 m
3. Area: 324 m²
o Side Length:
324=18\sqrt{324} = 18324=18 m
o Perimeter: 4×18=724
\times 18 = 724×18=72 m
4. Area: 400 m²
o Side Length:
400=20\sqrt{400} = 20400=20 m
o Perimeter: 4×20=804
\times 20 = 804×20=80 m
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