Pythagorean Theorem

The Pythagorean theorem (Pythagoras' theorem)
shows the relationship
between the sides of a right triangle.

a² + b² = c²

a, b: Legs
c: Hypotenuse

Pythagorean Theorem: Proof

The legs are 4 and 3.
The hypotenuse is x.

So, by the Pythagorean theorem,
x² = 4² + 3².

4² = 16
3² = 9

16 + 9 = 25

Square root both sides.

Then x = √25.

x is the lenght of the hypotenuse.
So x is plus.
So you don't have to write ± sign.

Quadratic Equation: Square Root

25 = 5²

√5² = 5

Simplify a Radical

So x = 5.

The legs are x and 5.
The hypotenuse is √89.

So, by the Pythagorean theorem,
x² + 5² + (√89)².

+5² = +25
(√89)² = 89

Move +25 to the right side.

Then x² = 64.

Square root both sides.

Then x = √64.

x is the lenght of the leg.
So x is plus.
So you don't have to write ± sign.

64 = 8²

√8² = 8

So x = 8.