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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Math worksheet on 'Pythagorean Theorem - Length of Side (Radical) (Level 2)'. Part of a broader unit on 'Pythagoras - Practice' Learn online: app.mobius.academy/math/units/pythagoras_practice/
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 p=square root of 252
b A LaTex expression showing p=square root of 180
c A LaTex expression showing p=square root of 324
d A LaTex expression showing p=square root of 108
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 m=square root of 383
b A LaTex expression showing m=square root of 95
c A LaTex expression showing m=square root of 239
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 x=square root of 167
b A LaTex expression showing x=square root of 311
c A LaTex expression showing x=square root of 23
d A LaTex expression showing x=square root of 265
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 z=square root of 239
b A LaTex expression showing z=square root of 95
c A LaTex expression showing z=square root of 383
d A LaTex expression showing z=square root of 481
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 x=square root of 44
b A LaTex expression showing x=square root of 532
c A LaTex expression showing x=square root of 244
d A LaTex expression showing x=square root of 188
e A LaTex expression showing x=square root of 332
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 652
b A LaTex expression showing d=square root of 132
c A LaTex expression showing d=square root of 328
d A LaTex expression showing d=square root of 260
e A LaTex expression showing d=square root of 524
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 x=square root of 142
b A LaTex expression showing x=square root of 21
c A LaTex expression showing x=square root of 263
d A LaTex expression showing x=square root of 463