np.sqrt() for square roots in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

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

np.sqrt() calculates the square root of each element in a numpy array or a single number.

beginner

How do you calculate the square root of 16 using numpy?

You use np.sqrt(16), which returns 4.0.

beginner

Can np.sqrt() handle arrays? Give an example.

Yes, it can. For example, np.sqrt(np.array([1, 4, 9])) returns [1. 2. 3.].

intermediate

What happens if you use np.sqrt() on a negative number?

It returns nan (not a number) and raises a warning because square root of negative numbers is not defined in real numbers.

beginner

Why is np.sqrt() useful in data science?

It helps to transform data, calculate distances, or normalize values by finding square roots quickly and efficiently.

What is the output of np.sqrt(25)?

A 25

B 5.0

C 12.5

D Error

The square root of 25 is 5, so np.sqrt(25) returns 5.0.

Which of these inputs can np.sqrt() accept?

A Single numbers and numpy arrays

B Only lists

C Only single numbers

D Only strings

np.sqrt() works with single numbers and numpy arrays, calculating square roots element-wise.

What does np.sqrt(np.array([4, 16, 36])) return?

A [1 2 3]

B [4 16 36]

C [2. 4. 6.]

D Error

It returns the square roots of each element: 2, 4, and 6.

What happens if you try np.sqrt(-9)?

A Returns nan or warning

B Returns 3

C Returns -3

D Returns 0

Square root of negative numbers is not defined in real numbers, so numpy returns nan and raises a warning.

Why might data scientists use np.sqrt()?

A To remove missing values

B To sort data

C To convert data to strings

D To calculate square roots for data transformation

Square roots help in data transformation, normalization, and distance calculations.

Explain how np.sqrt() works with both single numbers and arrays.

Think about how it handles one number versus many numbers.

Describe what happens when np.sqrt() is used on negative numbers and why.

Consider the math behind square roots and negative inputs.

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