[Term Entry] Add .sqrt() function documentation in PyTorch #8141

content/pytorch/concepts/tensor-operations/terms/sqrt/sqrt.md

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+---
+Title: '.sqrt()'
+Description: 'Computes the square root of each element in a PyTorch tensor.'
+Subjects:
+  - 'Data Science'
+  - 'Machine Learning'
+Tags:
+  - 'Deep Learning'
+  - 'Machine Learning'
+  - 'PyTorch'
+  - 'Tensors'
+CatalogContent:
+  - 'intro-to-py-torch-and-neural-networks'
+  - 'paths/computer-science'
+---
+
+The **`.sqrt()`** function in PyTorch computes the square root of each element in the input [tensor](https://www.codecademy.com/resources/docs/pytorch/tensors). This operation applies the mathematical function $\sqrt{x}$ element-wise to all values in the tensor.
+
+The square root function is commonly used in neural networks for normalization techniques, distance calculations (such as Euclidean distance), standard deviation computations, and various mathematical transformations in deep learning applications.
+
+## Syntax
+
+```pseudo
+torch.sqrt(input, *, out=None) → Tensor
+```
+
+**Parameters:**
+
+- `input`: The input tensor containing non-negative elements for which the square root will be computed.
+- `out` (optional): A tensor to store the output. If provided, the result is written to this tensor.
+
+**Return value:**
+
+Returns a new tensor where each element is the square root of the corresponding element in the input tensor.
+
+## Example 1: Applying `.sqrt()` to Single-Element and 1D Tensors
+
+This example shows how to compute the square root of both a scalar and a 1D tensor:
+
+```py
+import torch
+
+# Create a scalar tensor
+scalar = torch.tensor([16.0])
+result_scalar = torch.sqrt(scalar)
+
+print("Scalar input:", scalar)
+print("sqrt(16.0):", result_scalar)
+
+# Create a 1D tensor with various values
+x = torch.tensor([0.0, 1.0, 4.0, 9.0, 16.0, 25.0])
+result = torch.sqrt(x)
+
+print("\nInput tensor:", x)
+print("Square root:", result)
+```
+
+This produces the following output:
+
+```shell
+Scalar input: tensor([16.])
+sqrt(16.0): tensor([4.])
+
+Input tensor: tensor([ 0.,  1.,  4.,  9., 16., 25.])
+Square root: tensor([0., 1., 2., 3., 4., 5.])
+```
+
+> **Note:** $\sqrt{0} = 0$ and the square root function is only defined for non-negative real numbers. Attempting to compute the square root of negative numbers will result in `nan` (not a number) values.
+
+## Example 2: Applying `.sqrt()` to a Multi-Dimensional Array
+
+This example demonstrates computing the square root of a 2D tensor:
+
+```py
+import torch
+
+# Create a 2D tensor (3x3 matrix)
+x = torch.tensor([[1.0, 4.0, 9.0],
+                  [16.0, 25.0, 36.0],
+                  [49.0, 64.0, 81.0]])
+
+# Compute the square root
+result = torch.sqrt(x)
+
+print("Input tensor:")
+print(x)
+print("\nSquare root:")
+print(result)
+```
+
+This produces the following output:
+
+```shell
+Input tensor:
+tensor([[ 1.,  4.,  9.],
+        [16., 25., 36.],
+        [49., 64., 81.]])
+
+Square root:
+tensor([[1., 2., 3.],
+        [4., 5., 6.],
+        [7., 8., 9.]])
+```
+
+The `.sqrt()` function preserves the shape of the input tensor, applying the square root operation element-wise to each value in the multi-dimensional array. This is particularly useful when normalizing data or computing distance metrics in machine learning applications.