Pythagorean Equation from Squares - Length of Side (Radical)

Level 1

This math topic focuses on applying the Pythagorean theorem to find the length of the hypotenuse of a right triangle, with the sides' lengths given. It involves squaring the lengths of the two shorter sides, summing these squares, and then finding the square root of this sum to solve for the hypotenuse (c). The equations provided in the problems are represented both in text and visually with LaTeX expressions, and multiple choice answers are given for finding the radical (square root) of the hypotenuse. This practice helps reinforce foundational knowledge of the Pythagorean theorem.

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

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Squares - Length of Side (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 'a' in this equation

a2+22=62a^2 + 2^2 = 6^2

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Pythagorean Equation from Squares - Length of Side (Radical) Worksheet

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Math worksheet on 'Pythagorean Equation from Squares - Length of Side (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 'b' in this equation
A LaTex expression showing 3 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 55
b A LaTex expression showing b = square root of 183
c A LaTex expression showing b = square root of 119
2
Find the radical (square root) for the value of 'c' in this equation
A LaTex expression showing 5 to the power of 2 + 2 to the power of 2 = c to the power of 2
a A LaTex expression showing c = square root of 29
b A LaTex expression showing c = square root of 21
c A LaTex expression showing c = square root of 37
3
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 62
b A LaTex expression showing a = square root of 111
c A LaTex expression showing a = square root of 13
4
Find the radical (square root) for the value of 'c' in this equation
A LaTex expression showing 4 to the power of 2 + 4 to the power of 2 = c to the power of 2
a A LaTex expression showing c = square root of 32
b A LaTex expression showing c = square root of 0
c A LaTex expression showing c = square root of 64
5
Find the radical (square root) for the value of 'c' in this equation
A LaTex expression showing 6 to the power of 2 + 4 to the power of 2 = c to the power of 2
a A LaTex expression showing c = square root of 68
b A LaTex expression showing c = square root of 20
c A LaTex expression showing c = square root of 52
6
Find the radical (square root) for the value of 'c' in this equation
A LaTex expression showing 2 to the power of 2 + 5 to the power of 2 = c to the power of 2
a A LaTex expression showing c = square root of 21
b A LaTex expression showing c = square root of -21
c A LaTex expression showing c = square root of 54
d A LaTex expression showing c = square root of 29
7
Find the radical (square root) for the value of 'c' in this equation
A LaTex expression showing 6 to the power of 2 + 5 to the power of 2 = c to the power of 2
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 111