This math topic focuses on practicing the Pythagorean theorem by solving for the missing hypotenuse, denoted as 'c', in a right triangle using given side lengths 'a' and 'b'. Students apply the theorem to find the square root (radical) of the sum of the squares of the given side lengths, enhancing their foundational understanding of triangles and radicals. Each problem includes different values for 'a' and 'b,' and offers potential solutions for 'c', among which only one is correct based on Pythagoras' theorem. This topic helps strengthen students' skills in algebraic manipulation and applying geometric principles to find exact solutions.

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Pythagorean Equation from Variables - Either Missing Length (Radical) Worksheet

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Pythagorean Equation from Variables - Either Missing Length (Radical)
1
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 = 7
a A LaTex expression showing a = square root of 138
b A LaTex expression showing a = square root of 107
c A LaTex expression showing a = square root of 40
2
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 91
b A LaTex expression showing b = square root of 9
c A LaTex expression showing b = square root of 59
d A LaTex expression showing b = square root of 41
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 = 3\\b = ?\\c = 6
a A LaTex expression showing b = square root of 27
b A LaTex expression showing b = square root of 45
c A LaTex expression showing b = square root of 99
4
Find the radical (square root) for the value of 'c' 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 = 3\\c = ?
a A LaTex expression showing c = square root of 22
b A LaTex expression showing c = square root of 31
c A LaTex expression showing c = square root of 13
d A LaTex expression showing c = square root of 5
5
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 = 3\\c = ?
Find the radical (square root) for the value of 'c' in this equation
a A LaTex expression showing c = square root of 34
b A LaTex expression showing c = square root of 16
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 = 5\\b = ?\\c = 9
a A LaTex expression showing b = square root of 218
b A LaTex expression showing b = square root of 56
c A LaTex expression showing b = square root of 137
d A LaTex expression showing b = square root of 106
7
Find the radical (square root) for the value of 'c' 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 = 5\\c = ?
a A LaTex expression showing c = square root of 100
b A LaTex expression showing c = square root of 0
c A LaTex expression showing c = square root of 50
d A LaTex expression showing c = square root of 75
8
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 = 6\\c = 9
a A LaTex expression showing a = square root of 126
b A LaTex expression showing a = square root of 117
c A LaTex expression showing a = square root of 207
d A LaTex expression showing a = square root of 45