This math topic focuses on utilizing the Pythagorean theorem to find the radical (square root) of one side of a right triangle when given the lengths of the other two sides. The problems are structured to enhance skills in manipulating and solving for variables in algebraic expressions derived from geometric principles, specifically by squaring and square rooting within the context of the Pythagorean theorem. Students are required to isolate the variable, execute the necessary arithmetic operations, and determine the square root of the resulting values to find the unknown side length.

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Pythagorean Equation from Variables - Length of Side (Radical) Worksheet

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Math worksheet on 'Pythagorean Equation from Variables - Length of Side (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 a to the power of 2 + b to the power of 2 = c to the power of 2 \\a = 5\\b = ?\\c = 9
a A LaTex expression showing b = square root of 218
b A LaTex expression showing b = square root of 137
c A LaTex expression showing b = square root of 56
d A LaTex expression showing b = square root of 106
2
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + b to the power of 2 = c to the power of 2 \\a = ?\\b = 3\\c = 6
a A LaTex expression showing a = square root of 117
b A LaTex expression showing a = square root of 63
c A LaTex expression showing a = square root of 99
d A LaTex expression showing a = square root of 27
3
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + b to the power of 2 = c to the power of 2 \\a = ?\\b = 3\\c = 9
a A LaTex expression showing a = square root of 72
b A LaTex expression showing a = square root of 171
c A LaTex expression showing a = square root of 234
4
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + b to the power of 2 = c to the power of 2 \\a = ?\\b = 3\\c = 5
a A LaTex expression showing a = square root of 41
b A LaTex expression showing a = square root of 84
c A LaTex expression showing a = square root of 16
d A LaTex expression showing a = square root of 66
5
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + b to the power of 2 = c to the power of 2 \\a = ?\\b = 3\\c = 4
a A LaTex expression showing a = square root of 39
b A LaTex expression showing a = square root of 25
c A LaTex expression showing a = square root of 23
d A LaTex expression showing a = square root of 7
6
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing a to the power of 2 + b to the power of 2 = c to the power of 2 \\a = 6\\b = ?\\c = 8
a A LaTex expression showing b = square root of 92
b A LaTex expression showing b = square root of 156
c A LaTex expression showing b = square root of 28
7
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing a to the power of 2 + b to the power of 2 = c to the power of 2 \\a = 4\\b = ?\\c = 5
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 66
d A LaTex expression showing b = square root of 41
e A LaTex expression showing b = square root of 59