This math topic covers the application of the Pythagorean theorem to solve for missing side lengths in right triangles, specifically focusing on finding the square root of each side length from given equations. The problems present equations where students need to isolate and calculate the radical (square root) for the missing 'a' or 'b' values, given the sums of the squares of the other two sides. This practice integrates basic algebraic manipulations with the concepts of squares and square roots, aiding in building foundational skills in understanding Pythagorean relationships.

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

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Math worksheet on 'Pythagorean Equation from Squares - 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 + 2 to the power of 2 = 4 to the power of 2
a A LaTex expression showing a = square root of 36
b A LaTex expression showing a = square root of 44
c A LaTex expression showing a = square root of 28
d A LaTex expression showing a = square root of 12
e A LaTex expression showing a = square root of 20
2
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing 5 to the power of 2 + b to the power of 2 = 8 to the power of 2
a A LaTex expression showing b = square root of 167
b A LaTex expression showing b = square root of 39
c A LaTex expression showing b = square root of 217
d A LaTex expression showing b = square root of 89
3
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing 3 to the power of 2 + b to the power of 2 = 9 to the power of 2
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
d A LaTex expression showing b = square root of 171
4
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 = 7 to the power of 2
a A LaTex expression showing b = square root of 94
b A LaTex expression showing b = square root of 143
c A LaTex expression showing b = square root of 53
d A LaTex expression showing b = square root of 45
5
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 = 3 to the power of 2
a A LaTex expression showing a = square root of 5
b A LaTex expression showing a = square root of 31
c A LaTex expression showing a = square root of 14
d A LaTex expression showing a = square root of 23
6
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing 6 to the power of 2 + b to the power of 2 = 9 to the power of 2
a A LaTex expression showing b = square root of 126
b A LaTex expression showing b = square root of 207
c A LaTex expression showing b = square root of 45
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 = 9 to the power of 2
a A LaTex expression showing a = square root of 126
b A LaTex expression showing a = square root of 45
c A LaTex expression showing a = square root of 279
d A LaTex expression showing a = square root of 207
Pythagorean Equation from Squares - Either Missing Length (Radical) (Level 1) - Mobius Math