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When It Is Not Whole

Part of the Triangles section of Coddy's Geometry journey. Lesson 26 of 63.

Most right triangles do not have a whole-number hypotenuse. Legs 3 and 6 give c^2 = 9 + 36 = 45, and 45 is not a perfect square. The exact answer is the root itself, √(45), not a rounded decimal like 6.7.

$Right triangle PQR with legs 6 and 3$

A root can often be simplified. Look for a square number inside: 45 = 9 × 5, and the root of 9 is 3, so √(45) = 3×√(5). The 3 comes out in front and the 5 stays under the root. The board always writes a root in this simplest form.

Challenge

△ABC has a right angle at A. Find the exact length of BC, then press Check. The board gives the root in simplest form.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Triangles

2The Triangle Inequality

Can Three Sticks Meet?Exactly Reaching The Range of the Third Side The Formula Recap: The Third Side

5The Pythagorean Theorem

Squares on the Sides Finding the Hypotenuse Pythagorean TriplesWhen It Is Not WholeRecap: The Hypotenuse

8Special Right Triangles

The 45-45-90 Triangle Legs from the Hypotenuse The 30-60-90 Triangle All Three Sides Which Triangle Is It?Recap: Special Triangles

11Two Tools at Once

Height of an Isosceles Area from the Height The Equilateral Triangle Right Triangle Perimeter Recap: Two Tools