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.

more
View

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

Mobius Math Academy logo
Pythagorean Equation from Squares - Either Missing Length (Radical)
1
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 = 8 to the power of 2
a A LaTex expression showing b = square root of 48
b A LaTex expression showing b = square root of 208
c A LaTex expression showing b = square root of 112
d A LaTex expression showing b = square root of 176
e A LaTex expression showing b = square root of 144
2
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 = 6 to the power of 2
a A LaTex expression showing a = square root of 117
b A LaTex expression showing a = square root of 63
c A LaTex expression showing a = square root of 45
d A LaTex expression showing a = square root of 27
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 = 9 to the power of 2
a A LaTex expression showing b = square root of 146
b A LaTex expression showing b = square root of 178
c A LaTex expression showing b = square root of 65
d A LaTex expression showing b = square root of 227
4
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 = 8 to the power of 2
a A LaTex expression showing a = square root of 119
b A LaTex expression showing a = square root of 55
c A LaTex expression showing a = square root of 183
5
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 = 9 to the power of 2
a A LaTex expression showing b = square root of 77
b A LaTex expression showing b = square root of 239
c A LaTex expression showing b = square root of 158
6
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 = 8 to the power of 2
a A LaTex expression showing b = square root of 60
b A LaTex expression showing b = square root of 196
c A LaTex expression showing b = square root of 188
d A LaTex expression showing b = square root of 124
7
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 = 4 to the power of 2
a A LaTex expression showing b = square root of 7
b A LaTex expression showing b = square root of 25
c A LaTex expression showing b = square root of 39
d A LaTex expression showing b = square root of 23
8
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 = 7 to the power of 2
a A LaTex expression showing a = square root of 156
b A LaTex expression showing a = square root of 40
c A LaTex expression showing a = square root of 138