np.sqrt() for square roots in NumPy - Mini Project: Build & Apply

Calculate Square Roots Using np.sqrt()

📖 Scenario: You work in a bakery that wants to analyze the sizes of square cake pans. You have a list of areas of square pans, and you want to find the length of one side of each pan.

🎯 Goal: Use np.sqrt() to calculate the side lengths from the given areas.

📋 What You'll Learn

Create a numpy array called areas with the exact values: 16, 25, 36, 49, 64

Create a variable called side_lengths that stores the square roots of the areas array using np.sqrt()

Print the side_lengths array

💡 Why This Matters

🌍 Real World

Calculating square roots is useful in many fields like baking, construction, and science when you need to find side lengths from areas.

💼 Career

Data scientists often use numpy functions like <code>np.sqrt()</code> to quickly perform mathematical operations on data arrays.

1

Create the numpy array of areas

Import numpy as np and create a numpy array called areas with these exact values: 16, 25, 36, 49, 64

NumPy

import numpy as np
# Create the numpy array called areas with values 16, 25, 36, 49, 64
# Your code here

Hint

Use np.array() to create the array with the given numbers.

2

Prepare to calculate square roots

Create a variable called side_lengths and set it to None for now as a placeholder

NumPy

import numpy as np
areas = np.array([16, 25, 36, 49, 64])
side_lengths = None  # Your code here

Hint

This step sets up the variable before calculation.

3

Calculate the square roots using np.sqrt()

Use np.sqrt() on the areas array and assign the result to the variable side_lengths

NumPy

import numpy as np
areas = np.array([16, 25, 36, 49, 64])
side_lengths = None
# Calculate square roots of areas using np.sqrt() and assign to side_lengths
# Your code here

Hint

Call np.sqrt() with areas inside the parentheses.

4

Print the side lengths

Print the variable side_lengths to display the side lengths of the square pans

NumPy

import numpy as np
areas = np.array([16, 25, 36, 49, 64])
side_lengths = np.sqrt(areas)
# Print the side_lengths array
# Your code here

Hint

Use print(side_lengths) to show the results.

Practice

1. What does the np.sqrt() function do in NumPy?

easy

A. Calculates the square root of a number or each element in an array

B. Calculates the square of a number or each element in an array

C. Calculates the logarithm of a number or each element in an array

D. Calculates the exponential of a number or each element in an array

Solution

1. Step 1: Understand the function purpose

   np.sqrt() is designed to find the square root of numbers or arrays element-wise.

2. Step 2: Compare with other options

   Options B, C, and D describe different mathematical operations (square, logarithm, exponential) which are not what np.sqrt() does.

3. Final Answer:

   Calculates the square root of a number or each element in an array -> Option A

4. Quick Check:

   Square root = np.sqrt() [OK]

Hint: Remember: sqrt means square root, not square or log [OK]

Common Mistakes:

• Confusing square root with square
• Thinking it calculates logarithm
• Assuming it calculates exponential

2. Which of the following is the correct syntax to find the square root of 16 using NumPy?

easy

A. np.square(16)

B. np.sqrt(16)

C. np.sqrt16()

D. sqrt(np.16)

Solution

1. Step 1: Recall correct function usage

   The correct syntax to find the square root of a number is np.sqrt(number).

2. Step 2: Check each option

   np.sqrt(16) uses np.sqrt(16) which is correct. np.square(16) uses np.square(16) which squares the number, not square root. Options C and D have invalid syntax.

3. Final Answer:

   np.sqrt(16) -> Option B

4. Quick Check:

   Correct syntax = np.sqrt(value) [OK]

Hint: Use np.sqrt() with parentheses around the number [OK]

Common Mistakes:

• Using np.square() instead of np.sqrt()
• Missing parentheses after sqrt
• Incorrect function name or syntax

3. What is the output of the following code?

import numpy as np
arr = np.array([4, 9, 16])
result = np.sqrt(arr)
print(result)

medium

A. Error: np.sqrt() cannot take arrays

B. [16. 81. 256.]

C. [2. 3. 4.]

D. [1.414 3.0 4.0]

Solution

1. Step 1: Understand input array and function

   The array contains [4, 9, 16]. Applying np.sqrt() computes the square root of each element.

2. Step 2: Calculate square roots element-wise

   Square roots are sqrt(4)=2, sqrt(9)=3, sqrt(16)=4, so the result is [2. 3. 4.]

3. Final Answer:

   [2. 3. 4.] -> Option C

4. Quick Check:

   Square roots of [4,9,16] = [2,3,4] [OK]

Hint: np.sqrt() works element-wise on arrays [OK]

Common Mistakes:

• Confusing square root with square
• Expecting a single number output
• Thinking np.sqrt() cannot handle arrays

4. The following code raises a RuntimeWarning. What is the problem?

import numpy as np
arr = np.array([-4, 9, 16])
result = np.sqrt(arr)
print(result)

medium

A. np.sqrt() cannot handle negative numbers and raises a RuntimeWarning

B. The array syntax is incorrect

C. np.sqrt() requires a list, not a NumPy array

D. The print statement is missing parentheses

Solution

1. Step 1: Identify the input causing error

   The array contains a negative number -4. Square root of negative numbers is not defined for real numbers.

2. Step 2: Understand np.sqrt() behavior on negatives

   By default, np.sqrt() raises a RuntimeWarning and returns NaN for negative numbers. This causes unexpected output.

3. Final Answer:

   np.sqrt() cannot handle negative numbers and raises a RuntimeWarning -> Option A

4. Quick Check:

   Negative input to sqrt causes RuntimeWarning [OK]

Hint: Square root of negative numbers causes RuntimeWarnings unless complex dtype is used [OK]

Common Mistakes:

• Thinking array syntax is wrong
• Assuming np.sqrt() works on negatives by default
• Ignoring warning messages

5. You have a NumPy array arr = np.array([1, 4, 9, 16, 25]). You want to create a new array that contains the square roots of only the elements greater than 10. Which code correctly does this?

hard

A. np.sqrt(arr[arr < 10])

B. np.sqrt(arr) > 10

C. np.sqrt(arr) if arr > 10 else arr

D. np.sqrt(arr[arr > 10])

Solution

1. Step 1: Filter elements greater than 10

   Use boolean indexing arr > 10 to select elements 16 and 25.

2. Step 2: Apply np.sqrt() on filtered elements

   Apply np.sqrt() on the filtered array arr[arr > 10] to get square roots of 16 and 25, which are 4 and 5.

3. Final Answer:

   np.sqrt(arr[arr > 10]) -> Option D

4. Quick Check:

   Filter first, then sqrt on filtered [OK]

Hint: Filter array first, then apply np.sqrt() [OK]

Common Mistakes:

• Applying sqrt before filtering
• Using incorrect conditional syntax
• Filtering with wrong comparison operator