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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Pythagorean Equation from Variables - Length of Side (Radical)
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 = 7
a A LaTex expression showing b = square root of 123
b A LaTex expression showing b = square root of 73
c A LaTex expression showing b = square root of 122
d A LaTex expression showing b = square root of 24
e A LaTex expression showing b = square root of 74
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 = 2\\c = 8
a A LaTex expression showing a = square root of 132
b A LaTex expression showing a = square root of 124
c A LaTex expression showing a = square root of 60
d A LaTex expression showing a = square root of 188
3
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 106
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 218
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 = 6\\b = ?\\c = 8
a A LaTex expression showing b = square root of 156
b A LaTex expression showing b = square root of 92
c A LaTex expression showing b = square root of 28
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 = 7
a A LaTex expression showing b = square root of 111
b A LaTex expression showing b = square root of 62
c A LaTex expression showing b = square root of 13
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 = 2\\b = ?\\c = 5
a A LaTex expression showing b = square root of 21
b A LaTex expression showing b = square root of 79
c A LaTex expression showing b = square root of 71
d A LaTex expression showing b = square root of 46
7
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 = 5\\c = 6
a A LaTex expression showing a = square root of 61
b A LaTex expression showing a = square root of 47
c A LaTex expression showing a = square root of 83
d A LaTex expression showing a = square root of 11
8
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 = 8
a A LaTex expression showing b = square root of 167
b A LaTex expression showing b = square root of 103
c A LaTex expression showing b = square root of 89
d A LaTex expression showing b = square root of 39