Pythagorean Equation from Values - Either Missing Length (Radical)

Level 1

This math topic practices solving for missing lengths in right triangles using the Pythagorean theorem. Specifically, it focuses on isolating and calculating the radical (square root) values of sides given the sum of the squares of the other two sides in a right triangle equation format. The problems presented in varying complexity levels provide multiple-choice answers, which require students to select the correct radical value after calculating from rearranged Pythagorean equations. This forms part of introductory concepts to understanding Pythagoras' theorem.

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

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Values - Either Missing Length (Radical)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.


Find the radical (square root) for the value of 'b' in this equation

25+b2=3625 + b^2 = 36

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Pythagorean Equation from Values - Either Missing Length (Radical) Worksheet

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Math worksheet on 'Pythagorean Equation from Values - Either Missing Length (Radical) (Level 1)'. Part of a broader unit on 'Pythagoras - Foundations' Learn online: app.mobius.academy/math/units/pythagoras_foundations/
1
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + 4 = 16
a A LaTex expression showing a = square root of 44
b A LaTex expression showing a = square root of 36
c A LaTex expression showing a = square root of 28
d A LaTex expression showing a = square root of 12
2
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing 9 + b to the power of 2 = 81
a A LaTex expression showing b = square root of 72
b A LaTex expression showing b = square root of 153
c A LaTex expression showing b = square root of 234
d A LaTex expression showing b = square root of 171
3
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing 9 + b to the power of 2 = 49
a A LaTex expression showing b = square root of 138
b A LaTex expression showing b = square root of 107
c A LaTex expression showing b = square root of 89
d A LaTex expression showing b = square root of 40
4
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing 16 + b to the power of 2 = 25
a A LaTex expression showing b = square root of 9
b A LaTex expression showing b = square root of 34
c A LaTex expression showing b = square root of 41
d A LaTex expression showing b = square root of 59
5
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing 16 + b to the power of 2 = 81
a A LaTex expression showing b = square root of 227
b A LaTex expression showing b = square root of 97
c A LaTex expression showing b = square root of 259
d A LaTex expression showing b = square root of 178
e A LaTex expression showing b = square root of 65
6
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing 16 + b to the power of 2 = 36
a A LaTex expression showing b = square root of 20
b A LaTex expression showing b = square root of 56
c A LaTex expression showing b = square root of 92
d A LaTex expression showing b = square root of 88
e A LaTex expression showing b = square root of 124
7
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + 25 = 49
a A LaTex expression showing a = square root of 122
b A LaTex expression showing a = square root of 24
c A LaTex expression showing a = square root of 123
d A LaTex expression showing a = square root of 172