Either Missing Length (Radical) (Level 2)

This math topic focuses on using the Pythagorean Theorem to find the length of missing sides in various two-dimensional shapes, with answers presented as square root values. It introduces participants to foundational concepts in dealing with three-dimensional geometric scenarios by applying this classic theorem to find unknown lengths, enhancing their skills in algebraic manipulation and understanding of radical expressions. The problems are structured to develop and reinforce the ability to calculate precise side lengths necessary for more complex geometry involved in three-dimensional spaces.

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

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Pythagorean Theorem - Either Missing Length (Radical) Worksheet

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Pythagorean Theorem - Either Missing Length (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 x=square root of 313
b A LaTex expression showing x=square root of 57
c A LaTex expression showing x=square root of 185
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 145
b A LaTex expression showing r=square root of 273
c A LaTex expression showing r=square root of 17
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 368
b A LaTex expression showing r=square root of 80
c A LaTex expression showing r=square root of 224
d A LaTex expression showing r=square root of 496
4
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 y=square root of 19
b A LaTex expression showing y=square root of 181
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 n=square root of 115
b A LaTex expression showing n=square root of 669
c A LaTex expression showing n=square root of 507
d A LaTex expression showing n=square root of 311
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 328
b A LaTex expression showing d=square root of 260
c A LaTex expression showing d=square root of 524
d A LaTex expression showing d=square root of 132
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 y=square root of 39
b A LaTex expression showing y=square root of 139
c A LaTex expression showing y=square root of 89
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 y=square root of 513
b A LaTex expression showing y=square root of 351
c A LaTex expression showing y=square root of 207
d A LaTex expression showing y=square root of 63