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

16+b2=2516 + b^2 = 25

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 + 9 = 64
a A LaTex expression showing a = square root of 119
b A LaTex expression showing a = square root of 55
c A LaTex expression showing a = square root of 137
d A LaTex expression showing a = square root of 183
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 144
b A LaTex expression showing b = square root of 176
c A LaTex expression showing b = square root of 80
d A LaTex expression showing b = square root of 48
3
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 144
b A LaTex expression showing a = square root of 112
c A LaTex expression showing a = square root of 176
d A LaTex expression showing a = square root of 48
4
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + 36 = 49
a A LaTex expression showing a = square root of 134
b A LaTex expression showing a = square root of 13
c A LaTex expression showing a = square root of 62
5
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 41
b A LaTex expression showing a = square root of 66
c A LaTex expression showing a = square root of 16
6
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + 36 = 81
a A LaTex expression showing a = square root of 45
b A LaTex expression showing a = square root of 126
c A LaTex expression showing a = square root of 207
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 = 81
a A LaTex expression showing a = square root of 218
b A LaTex expression showing a = square root of 268
c A LaTex expression showing a = square root of 56
d A LaTex expression showing a = square root of 187
e A LaTex expression showing a = square root of 137