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Pythagorean Equation from Squares - Either Missing Length (Radical) (Level 1)

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.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Squares - Either Missing Length (Radical)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Find the radical (square root) for the value of 'b' in this equation

42+b2=724^2 + b^2 = 7^2

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 + 6 to the power of 2 = 7 to the power of 2
a A LaTex expression showing a = square root of 13
b A LaTex expression showing a = square root of 85
c A LaTex expression showing a = square root of 62
2
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 72
b A LaTex expression showing b = square root of 153
c A LaTex expression showing b = square root of 90
d A LaTex expression showing b = square root of 252
3
Find the radical (square root) for the value of 'b' in this equation
A LaTex expression showing 4 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 114
b A LaTex expression showing b = square root of 33
c A LaTex expression showing b = square root of 65
d A LaTex expression showing b = square root of 131
4
Find the radical (square root) for the value of 'a' in this equation
A LaTex expression showing a to the power of 2 + 4 to the power of 2 = 6 to the power of 2
a A LaTex expression showing a = square root of 20
b A LaTex expression showing a = square root of 56
c A LaTex expression showing a = square root of 92
d A LaTex expression showing a = square root of 88
5
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 = 5 to the power of 2
a A LaTex expression showing b = square root of 66
b A LaTex expression showing b = square root of 41
c A LaTex expression showing b = square root of 16
d A LaTex expression showing b = square root of 34
6
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 7
b A LaTex expression showing a = square root of 25
c A LaTex expression showing a = square root of 23
d A LaTex expression showing a = square root of 39
7
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 = 7 to the power of 2
a A LaTex expression showing b = square root of 13
b A LaTex expression showing b = square root of 62
c A LaTex expression showing b = square root of 111