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Pythagorean Equation from Variables - Length of Side (Radical) (Level 1)

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.

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

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Variables - Length of Side (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 'a' in this equation

a2+b2=c2a=?b=3c=8a^2 + b^2 = c^2\\a = ?\\b = 3\\c = 8

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 = 2\\b = ?\\c = 5
a A LaTex expression showing b = square root of 71
b A LaTex expression showing b = square root of 46
c A LaTex expression showing b = square root of 21
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 = 4\\c = 7
a A LaTex expression showing a = square root of 163
b A LaTex expression showing a = square root of 33
c A LaTex expression showing a = square root of 82
d A LaTex expression showing a = square root of 131
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 = 2\\c = 7
a A LaTex expression showing a = square root of 102
b A LaTex expression showing a = square root of 45
c A LaTex expression showing a = square root of 94
d A LaTex expression showing a = square root of 143
4
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 = 2\\b = ?\\c = 7
a A LaTex expression showing b = square root of 143
b A LaTex expression showing b = square root of 45
c A LaTex expression showing b = square root of 53
d A LaTex expression showing b = square root of 94
5
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 164
b A LaTex expression showing b = square root of 156
c A LaTex expression showing b = square root of 92
d A LaTex expression showing b = square root of 28
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 = 4\\b = ?\\c = 6
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
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 = 6\\b = ?\\c = 7
a A LaTex expression showing b = square root of 13
b A LaTex expression showing b = square root of 111
c A LaTex expression showing b = square root of 62