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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Math worksheet on 'Pythagorean Equation from Variables - Either Missing Length (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 '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 = 8
a A LaTex expression showing a = square root of 217
b A LaTex expression showing a = square root of 39
c A LaTex expression showing a = square root of 167
d A LaTex expression showing a = square root of 103
2
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 = 3\\b = 6\\c = ?
a A LaTex expression showing c = square root of 81
b A LaTex expression showing c = square root of 27
c A LaTex expression showing c = square root of 45
d A LaTex expression showing c = square root of -27
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 = 9
a A LaTex expression showing b = square root of 234
b A LaTex expression showing b = square root of 72
c A LaTex expression showing b = square root of 153
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 = 6\\b = 6\\c = ?
a A LaTex expression showing c = square root of 72
b A LaTex expression showing c = square root of 0
c A LaTex expression showing c = square root of 144
d A LaTex expression showing c = square root of 108
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 = 2\\c = 6
a A LaTex expression showing a = square root of 104
b A LaTex expression showing a = square root of 40
c A LaTex expression showing a = square root of 68
d A LaTex expression showing a = square root of 32
6
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 13
c A LaTex expression showing c = square root of 5
d A LaTex expression showing c = square root of 31
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 = 5\\b = ?\\c = 9
a A LaTex expression showing b = square root of 56
b A LaTex expression showing b = square root of 137
c A LaTex expression showing b = square root of 218
d A LaTex expression showing b = square root of 106