Mathematics for GIS Professionals

Squares, Cubes and Roots

Squares and square roots come in very handy in geography when using the theorem of Pythagoras to calculate the distance between two points based on a right-angled triangle. The theorem of Pythagoras states that in any right-angled triangle, the square of the diagonal (hypotenuse) is equal to the sum of the squares of the shorter sides of the triangle. In geography if we have two points, $A$ and $B$ on the Cartesian plane (x – horizontal axis and y- vertical axis) and their coordinates are known then the differences in the coordinates in the x-direction $(M)$ and y-direction $(N)$ can be used to calculate the distance between them.

Distance between  $A$ and $B$ = $M^2 + N^2$

The square of 5 is $5^2 = 25$ because $5^2 = 5^1 \times 5^1 =25$

The square root of 4 id $\sqrt{4}=2$ because $4=2 \times 2$

The square of the expression $a^3$ is $(a^3)^2 = a^3a^3 = a^{3+3}=a^6$

The square root of $36x^8$ is $\sqrt{36x^8} = 6x^4$ because $6x^4 \times 6x^4 = 36x^8$

Using the laws of exponents $a^{\frac{1}{2}} = \sqrt{a}$ and $a^{\frac{3}{2}} = \sqrt{a^3}$

Two cubed, means $2^3 = 2\times 2 \times 2 = 8$

The cube root of 8 is $\sqrt[3]{8} = 2$

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