Length of Side (Radical) (Level 1)

This math topic focuses on the application of the Pythagorean theorem to find the length of a missing side of a triangle, expressed in radical form (i.e., square roots). It serves as an introductory exploration into the Pythagorean theorem, aiming to deepen understanding of the relationship between the sides of right-angled triangles. The problems presented require students to calculate and express answers as radicals, bolstering their skills in both geometry and algebraic manipulation. Each question features a diagram of a right triangle with dimensions provided, prompting the student to solve for the unknown side.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Pythagorean Theorem - Length of Side (Radical) Worksheet

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Pythagorean Theorem - Length of Side (Radical)
1
Find the length of the missing side as a square root value, based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing n=square root of 126
b A LaTex expression showing n=square root of 198
c A LaTex expression showing n=square root of 207
d A LaTex expression showing n=square root of 45
2
Find the length of the missing side as a square root value, based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing r=square root of 52
b A LaTex expression showing r=square root of 28
c A LaTex expression showing r=square root of 12
d A LaTex expression showing r=square root of 44
3
Find the length of the missing side as a square root value, based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing r=square root of 134
b A LaTex expression showing r=square root of 62
c A LaTex expression showing r=square root of 13
d A LaTex expression showing r=square root of 111
4
Find the length of the missing side as a square root value, based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing y=square root of 85
b A LaTex expression showing y=square root of 278
c A LaTex expression showing y=square root of 157
d A LaTex expression showing y=square root of 327
5
Find the length of the missing side as a square root value, based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing r=square root of 176
b A LaTex expression showing r=square root of 80
c A LaTex expression showing r=square root of 144
d A LaTex expression showing r=square root of 48
6
Find the length of the missing side as a square root value, based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing m=square root of 284
b A LaTex expression showing m=square root of 84
c A LaTex expression showing m=square root of 216
d A LaTex expression showing m=square root of 184
7
Find the length of the missing side as a square root value, based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing r=square root of 105
b A LaTex expression showing r=square root of 347
c A LaTex expression showing r=square root of 379
d A LaTex expression showing r=square root of 226
8
Find the length of the missing side as a square root value, based on the Pythagorean theorem
An svg image showing a math problem
a A LaTex expression showing x=square root of 71
b A LaTex expression showing x=square root of 21
c A LaTex expression showing x=square root of 29
d A LaTex expression showing x=square root of 54