Length of Side (Radical) (Level 2)

This topic focuses on applying the Pythagorean theorem to find the length of a missing side of a triangle, with the solution expressed as a square root value. Students are tasked with solving multiple problems where they need to calculate the missing length based on the given sides of a right-angled triangle. Each problem requires understanding and manipulating radicals as part of the solution process. This set of problems is part of an introductory unit on Pythagoras' theorem.

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 z=square root of 217
b A LaTex expression showing z=square root of 459
c A LaTex expression showing z=square root of 48
d A LaTex expression showing z=square root of 386
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 d=square root of 239
b A LaTex expression showing d=square root of 95
c A LaTex expression showing d=square root of 383
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 d=square root of 221
b A LaTex expression showing d=square root of 263
c A LaTex expression showing d=square root of 21
d A LaTex expression showing d=square root of 142
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 x=square root of 332
b A LaTex expression showing x=square root of 188
c A LaTex expression showing x=square root of 532
d A LaTex expression showing x=square root of 44
e A LaTex expression showing x=square root of 244
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 y=square root of 274
b A LaTex expression showing y=square root of 443
c A LaTex expression showing y=square root of 105
d A LaTex expression showing y=square root of 402
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 d=square root of 265
b A LaTex expression showing d=square root of 167
c A LaTex expression showing d=square root of 23
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 p=square root of 513
b A LaTex expression showing p=square root of 207
c A LaTex expression showing p=square root of 369
d A LaTex expression showing p=square root of 63
e A LaTex expression showing p=square root of 351
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 p=square root of 427
b A LaTex expression showing p=square root of 57
c A LaTex expression showing p=square root of 178