TicTacMaths: noviembre 2017

Para este nuevo tema, os dejo bastantes recursos de teoría en la carpeta, así como algunos enlaces para que aprendáis de una forma más didáctica y divertida.
Os dejo además abajo un resumen inicial.
Espero que estemos dispuestos a trabajar duro este tema.
Vídeo explicativo:
http://my.hrw.com/math06_07/nsmedia/homework_help/msm3/msm3_ch04_03_homeworkhelp.html
Nos vemos en las aulas.
E*
PARA PRACTICAR: http://grc.anaya.es/grc/act/e8425133/1469011407/index.html
http://recursostic.educacion.es/descartes/web/materiales_didacticos/Powers_roots/index.htm

Powers

When we want to multiply a number by itself we use powers.

For example, the quantity 7⁴= 7 × 7 × 7 × 7. The number 4 tells us the number of times to be multiplied 7 by itself. In this example, the index or exponent is 4. The number 7 is called base.

Example
6² = 6 × 6 = 36. We say that ‘6 squared is 36’, or ‘6 raised to the power 2 is 36’.
2⁵ = 2 × 2 × 2 × 2 × 2 = 32. We say that ‘2 to the power 5 is 32’.

Properties of the powers

·     Power of a Power Property: This property states that the power of a power can be found by multiplying the exponents.

(a^m)ⁿ = a^mn(2²)³ = 2^2×3 = 2⁶ = 64

·     Product of Powers Property: This property states that to multiply powers having the same base, add the exponents.

a^m · aⁿ= a^m+n2²× 2⁵ = 2²⁺⁵ = 2⁷ = 128

·     Quotient of Powers Property: This property states that to divide powers having the same base, subtract the exponents.

a^m : aⁿ= a^m-n5⁴: 5³ = 5^4-3 = 5¹ = 5

·     Power of a Product Property: This property states that the power of a product can be obtained by finding the powers of each factor and multiplying them.

(ab)^m = a^m · b^m(3 × 4)² = 3²× 4² = 9 × 16 = 144

·     Power of a Quotient Property: This property states that the power of a quotient can be obtained by finding the powers of numerator and denominator and dividing them.

(a/b)^m = a^m / b^m (8 : 2)² = 8² :2² = 64 : 4 = 16

Perfect squares

A square number, sometimes also called a perfect square, is an integer that is the square of another integer number.

So, for example, 9 is a square number, since it can be written as 3²; 9 =3²
Other square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81....

Square roots

When 5 is squared we obtain 25. That is 5² = 25.

The reverse of this process is called finding a square root. The square root of 25 is 5, because  5²= 25 This is written as

Note also that when −5 is squared we again obtain 25, that is (-5)²= 25. This means that 25 has another square root, −5.

In general, a square root of a number is a number which when squared gives the original number.

There are always two square roots of any positive number, one positive and one negative:

Therefore, negative numbers do not have any square roots.