This math topic focuses on applying the Pythagorean theorem to find the hypotenuse of a right triangle, expressing the results in radical form. Each problem gives the values for legs \(a\) and \(b\), and students must calculate the length of hypotenuse \(c\) by finding the square root of the sum of the squares of \(a\) and \(b\). Various questions provide different sets of numerical values for \(a\) and \(b\), requiring learners to compute \(c\) as a radical expression, with multiple-choice format for answers. This forms a fundamental part of understanding the principles of the Pythagorean theorem in geometry.

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

more
View

Pythagorean Equation from Variables - Length of Hypotenuse (Radical) Worksheet

Mobius Math Academy logo
Math worksheet on 'Pythagorean Equation from Variables - Length of Hypotenuse (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 '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 = 4\\b = 5\\c = ?
a A LaTex expression showing c = square root of 9
b A LaTex expression showing c = square root of -9
c A LaTex expression showing c = square root of 41
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 = 2\\b = 3\\c = ?
a A LaTex expression showing c = square root of 13
b A LaTex expression showing c = square root of -5
c A LaTex expression showing c = square root of 31
d A LaTex expression showing c = square root of 22
e A LaTex expression showing c = square root of 5
3
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 = 5\\c = ?
a A LaTex expression showing c = square root of 54
b A LaTex expression showing c = square root of 29
c A LaTex expression showing c = square root of 21
d A LaTex expression showing c = square root of 79
4
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 = ?
Find the radical (square root) for the value of 'c' in this equation
a A LaTex expression showing c = square root of 27
b A LaTex expression showing c = square root of 45
5
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 = 4\\c = ?
a A LaTex expression showing c = square root of 57
b A LaTex expression showing c = square root of 9
c A LaTex expression showing c = square root of 41
6
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 = 4\\c = ?
Find the radical (square root) for the value of 'c' in this equation
a A LaTex expression showing c = square root of 52
b A LaTex expression showing c = square root of 20
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 = 6\\b = 5\\c = ?
a A LaTex expression showing c = square root of 11
b A LaTex expression showing c = square root of 61
c A LaTex expression showing c = square root of 86
d A LaTex expression showing c = square root of 111
Pythagorean Equation from Variables - Length of Hypotenuse (Radical) (Level 1) - Mobius Math