Length of Hypotenuse (Radical) (Level 2)

This math topic focuses on practicing the Pythagorean Theorem, specifically calculating the lengths of missing sides of triangles presented as radical values (square roots). Each problem requires using the theorem to find the length of one or more sides of a right triangle, with answers given in exact square root notation. The problems are intended to reinforce understanding of geometric relationships and algebraic manipulation involving square roots, as well as provide visualization and application of the Pythagorean Theorem in diverse scenarios.

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

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Pythagorean Theorem - Length of Hypotenuse (Radical) Worksheet

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Pythagorean Theorem - Length of Hypotenuse (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 221
b A LaTex expression showing z=square root of 342
c A LaTex expression showing z=square root of 21
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 185
b A LaTex expression showing m=square root of 57
c A LaTex expression showing m=square root of -57
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 n=square root of 484
b A LaTex expression showing n=square root of 0
c A LaTex expression showing n=square root of 242
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 181
b A LaTex expression showing y=square root of 19
c A LaTex expression showing y=square root of -19
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 p=square root of 116
b A LaTex expression showing p=square root of 316
c A LaTex expression showing p=square root of 84
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 p=square root of 40
b A LaTex expression showing p=square root of 202
c A LaTex expression showing p=square root of 364
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 80
b A LaTex expression showing x=square root of 144
c A LaTex expression showing x=square root of 48
8
An svg image showing a math problem
Find the length of the missing side as a square root value, based on the Pythagorean theorem
a A LaTex expression showing n=square root of 72
b A LaTex expression showing n=square root of 170