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# 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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Edzai Conilias Zvobwo is passionate about empowering Africans through mathematics, problem-solving techniques and media. As such, he founded MathsGee. Through this organisation, he has helped create an ecosystem for disseminating information, training, and supporting STEM education to all African people. A maths evangelist who teaches mathematical thinking as a life skill, Edzai’s quest has seen him being named the SABC Ambassador for STEM; he has been invited to address Fortune 500 C-suite executives at the Mobile 360 North America; was nominated to represent Southern Africa at the inaugural United Nations Youth Skills Day in New York; was invited to be a contributor to the World Bank Group Youth Summit in 2016; has won the 2014 SADC Protocol on Gender and Development award for his contribution to women’s empowerment in education; and has partnered with local and global firms in STEM interventions.