Squares and Square Roots, The Pythagorean Theorem

Squares & Square Roots

–          a² = squaring

*If a² = b, then a is called the square root of b

*PERFECT SQUARES are called “perfect”, because they have whole numbers as square roots. To find the square root of a number, think about which factor when multiplied by itself will give you that square. Ex: √64 = 8 because 8² = 64

*When finding the square root of a nonperfect square, you can approximate between two numbers. Ex: √28  –  this is between  √25 and √36, so your answer is between 5 and 6.

The Pythagorean Theorem

The Pythagorean Theorem states that: The square of the measure of the hypotenuse of a right triangle is equal to the sum of the squares of the measures of the two other sides.

Hypotenuse – the side opposite of the right angle

Simply, a² + b² = c²

or leg² + leg² = hypotenuse²

Using what we know about squares, lets see an example:

If a=3, b=4, find c.

a² + b² = c²

3² + 4² = c²

9 + 16 = c²

25 = c²

Something squared will give us 25. You can either guess and check, or you can find the square root of 25

√25 = √c²

5 = c

Sometimes, instead of being given the lengths of the two legs, you will be given the length of one leg and the hypotenuse.

Ex: If a=3, c=5, find b.

a² + b² = c²

3² + b² = 5²

9 + b² = 25

9 + b² = 25

9 + 16 = 25

√16 = 4

b = 4

Common Pythagorean Triples:

3:4:5   5:12:13   8:15:17   7:24:25   9:40:41