Squares and Roots

Thursday, September 18, 2014

$\small \sqrt[1]{1}^{1}$

Part One: Basic Theories of Squares and Roots

In learning about squares and roots, first we must understand and grasp the basics firmly. In the introduction module we have learnt about the most basic forms of exponents, and below are the basic theories in squares and roots. These are very elementary; To excel in this area you must completely understand these.

A number with a positive square is the same number multiplied repeatedly.

$2^{3} = 2\times 2 \times2$

The division between 2 numbers with the same base is the subtraction of the squares.

$2^{5} \div 2^{3} = 2^{5-3} = 2^{2}$

The multiplication of 2 numbers with the same base is the sum of the squares.
$\small 2^{5} \times 2^{3} = 2^{5 + 3} = 2^{8}$

A square in a square can be multiplied.
$\small ((2^{3})^{4}) = 2^{3\times 4} = 2^{12}$

Multiplication of the same square number:
$\small 3^{5} \times 6^{5} = 18^{5} = 1889568$

Division of the same square number
$\small 6^{5} : 3^{5} = 2^{5} = 32$

From the division of squares, we found negative square:

$\small 2^{3} : 2^{5} = 2^{3-5} = 2^{-2}$

$\small \frac{2^{3}}{2^{5}} = \frac{2\times 2\times 2}{2\times 2\times 2\times 2\times 2} = \frac{1}{2\times 2} = \frac{1}{2^{2}}$

$\small \frac{1}{2^{2}} = 2^{-2}$

Root is a fractional square

$\small \sqrt[5]{863} = 863^{\frac{1}{5}}$

Roots and squares can be combined into 1

Swiss Cheese Math

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Squares and Roots

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