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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

4+b2=164 + b^2 = 16

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 'b' in this equation
A LaTex expression showing 4 + b to the power of 2 = 25
a A LaTex expression showing b = square root of 21
b A LaTex expression showing b = square root of 71
c A LaTex expression showing b = square root of 46
d A LaTex expression showing b = square root of 29
2
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing 16 + b to the power of 2 = 64
a A LaTex expression showing b = square root of 80
b A LaTex expression showing b = square root of 48
c A LaTex expression showing b = square root of 176
d A LaTex expression showing b = square root of 144
3
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + 9 = 25
a A LaTex expression showing a = square root of 16
b A LaTex expression showing a = square root of 41
c A LaTex expression showing a = square root of 66
4
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + 16 = 64
a A LaTex expression showing a = square root of 176
b A LaTex expression showing a = square root of 112
c A LaTex expression showing a = square root of 144
d A LaTex expression showing a = square root of 48
5
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + 25 = 81
a A LaTex expression showing a = square root of 187
b A LaTex expression showing a = square root of 56
c A LaTex expression showing a = square root of 268
d A LaTex expression showing a = square root of 218
e A LaTex expression showing a = square root of 137
6
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + 4 = 81
a A LaTex expression showing a = square root of 77
b A LaTex expression showing a = square root of 166
c A LaTex expression showing a = square root of 85
d A LaTex expression showing a = square root of 158
e A LaTex expression showing a = square root of 239
7
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing 4 + b to the power of 2 = 9
a A LaTex expression showing b = square root of 5
b A LaTex expression showing b = square root of 22
c A LaTex expression showing b = square root of 13
d A LaTex expression showing b = square root of 14