Pythagorean Theorem - Length of Hypotenuse - Labelled Sides (Radical) (Level 2)

This math topic focuses on the application of the Pythagorean Theorem to find the lengths of missing sides in right triangles, specifically the hypotenuse. The problems require expressing the lengths as square root values and utilize labeled sides. These exercises help enhance skills in identifying the sides of triangles, applying the theorem formula \(a^2 + b^2 = c^2\), and simplifying radical expressions. The problems progress through a set of examples, providing solutions in radical form, thus deepening understanding of Pythagorean relationships and radical calculations.

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

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Length of Hypotenuse - Labelled Sides (Radical)

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Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²

c = ?b = 11a = 8

Pythagorean Theorem - Length of Hypotenuse - Labelled Sides (Radical) Worksheet

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Math worksheet on 'Pythagorean Theorem - Length of Hypotenuse - Labelled Sides (Radical) (Level 2)'. Part of a broader unit on 'Pythagoras - Intro' Learn online: app.mobius.academy/math/units/pythagoras_intro/
1
An svg image showing a math problem
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
a A LaTex expression showing square root of 17
b A LaTex expression showing square root of 145
2
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing square root of 36
b A LaTex expression showing square root of 264
c A LaTex expression showing square root of 164
d A LaTex expression showing square root of 364
3
An svg image showing a math problem
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
a A LaTex expression showing square root of 185
b A LaTex expression showing square root of 57
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: a² + b² = c²
a A LaTex expression showing square root of 130
b A LaTex expression showing square root of 32
5
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing square root of 106
b A LaTex expression showing square root of -56
c A LaTex expression showing square root of 56
d A LaTex expression showing square root of 268
6
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing square root of 148
b A LaTex expression showing square root of 116
c A LaTex expression showing square root of 84
7
Find the length of the missing side as a square root value, based on the Pythagorean theorem: a² + b² = c²
An svg image showing a math problem
a A LaTex expression showing square root of 221
b A LaTex expression showing square root of 421
c A LaTex expression showing square root of 21