This math topic focuses on applying the Pythagorean theorem to find the length of the hypotenuse of a right triangle, with the sides' lengths given. It involves squaring the lengths of the two shorter sides, summing these squares, and then finding the square root of this sum to solve for the hypotenuse (c). The equations provided in the problems are represented both in text and visually with LaTeX expressions, and multiple choice answers are given for finding the radical (square root) of the hypotenuse. This practice helps reinforce foundational knowledge of the Pythagorean theorem.

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

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Pythagorean Equation from Squares - Length of Side (Radical)
1
Find the radical (square root) for the value of 'c' in this equation
A LaTex expression showing 4 to the power of 2 + 5 to the power of 2 = c to the power of 2
a A LaTex expression showing c = square root of 41
b A LaTex expression showing c = square root of -9
c A LaTex expression showing c = square root of 9
2
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing 2 to the power of 2 + b to the power of 2 = 5 to the power of 2
a A LaTex expression showing b = square root of 54
b A LaTex expression showing b = square root of 21
c A LaTex expression showing b = square root of 46
d A LaTex expression showing b = square root of 71
3
Find the radical (square root) for the value of 'c' in this equation
A LaTex expression showing 3 to the power of 2 + 6 to the power of 2 = c to the power of 2
a A LaTex expression showing c = square root of 45
b A LaTex expression showing c = square root of 27
c A LaTex expression showing c = square root of -27
d A LaTex expression showing c = square root of 81
4
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + 2 to the power of 2 = 8 to the power of 2
a A LaTex expression showing a = square root of 196
b A LaTex expression showing a = square root of 60
c A LaTex expression showing a = square root of 188
5
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + 3 to the power of 2 = 4 to the power of 2
a A LaTex expression showing a = square root of 39
b A LaTex expression showing a = square root of 7
c A LaTex expression showing a = square root of 23
d A LaTex expression showing a = square root of 41
6
Find the radical (square root) for the value of 'c' in this equation
A LaTex expression showing 4 to the power of 2 + 3 to the power of 2 = c to the power of 2
a A LaTex expression showing c = square root of 43
b A LaTex expression showing c = square root of 25
c A LaTex expression showing c = square root of 7
7
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + 6 to the power of 2 = 7 to the power of 2
a A LaTex expression showing a = square root of 111
b A LaTex expression showing a = square root of 134
c A LaTex expression showing a = square root of 13
8
Find the radical (square root) for the value of 'c' in this equation
A LaTex expression showing 2 to the power of 2 + 5 to the power of 2 = c to the power of 2
a A LaTex expression showing c = square root of 79
b A LaTex expression showing c = square root of 21
c A LaTex expression showing c = square root of -21
d A LaTex expression showing c = square root of 29