np.sqrt() for square roots in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of np.sqrt() on a 1D array

What is the output of this code?

import numpy as np
arr = np.array([1, 4, 9, 16])
result = np.sqrt(arr)
print(result)

NumPy

import numpy as np
arr = np.array([1, 4, 9, 16])
result = np.sqrt(arr)
print(result)

A [1 4 9 16]

B [1 2 3 4]

C [1.0 2.0 3.0 4.0]

D [1. 2. 3. 4.]

💡 Hint

np.sqrt() returns floating point numbers even if input is integers.

np.sqrt() calculates the square root element-wise and returns floats. So the output is an array of floats: [1. 2. 3. 4.]

❓ data_output

intermediate

Shape and values after np.sqrt() on 2D array

Given this code, what is the shape and content of result?

import numpy as np
arr = np.array([[4, 9], [16, 25]])
result = np.sqrt(arr)
print(result.shape)
print(result)

NumPy

import numpy as np
arr = np.array([[4, 9], [16, 25]])
result = np.sqrt(arr)
print(result.shape)
print(result)

A

(2, 2) and [[4. 9.]
 [16. 25.]]

B (4,) and [2. 3. 4. 5.]

C

(2, 2) and [[2. 3.]
 [4. 5.]]

D

(2, 2) and [[2 3]
 [4 5]]

💡 Hint

np.sqrt keeps the shape of the input array and returns floats.

The input is a 2x2 array. np.sqrt returns the square root element-wise, keeping the shape (2,2) and converting values to floats.

🔧 Debug

advanced

Error when applying np.sqrt() to negative numbers

What error or warning does this code produce?

import numpy as np
arr = np.array([-1, 4, 9])
result = np.sqrt(arr)
print(result)

NumPy

import numpy as np
arr = np.array([-1, 4, 9])
result = np.sqrt(arr)
print(result)

A

RuntimeWarning: invalid value encountered in sqrt
[nan 2. 3.]

B ValueError: math domain error

C TypeError: unsupported operand type(s) for sqrt

D [-1. 2. 3.]

💡 Hint

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

np.sqrt on negative values returns nan and raises a RuntimeWarning about invalid value encountered.

🧠 Conceptual

advanced

Understanding np.sqrt() output type

If you apply np.sqrt() to an integer numpy array, what is the data type of the output array?

A Float type array

B Integer type array

C Boolean type array

D Complex type array

💡 Hint

Square roots often produce decimal numbers, so output must support decimals.

np.sqrt converts integer inputs to floats because square roots can be decimal numbers.

🚀 Application

expert

Using np.sqrt() to normalize data

You have a numpy array of positive values representing counts:

counts = np.array([1, 4, 9, 16, 25])

You want to apply square root transformation to reduce skewness before analysis.
Which code snippet correctly applies this transformation and stores the result in transformed?

A transformed = counts ** 2

B transformed = np.sqrt(counts)

C transformed = np.square(counts)

D transformed = np.sqrt(counts) * 2

💡 Hint

Square root transformation means applying np.sqrt directly.

Applying np.sqrt reduces skewness by compressing large values more than small ones.

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