According to Sal Khan and Monterey Institute for Technology and Education (2011), radical are equation is an equation that has its unknown values appear under a radical sign. As such, the number of unknown values can vary in number. Sal Khan and Monterey Institute for Technology and Education (2011) focus on the explanation of the steps involved in the simplification of the variable of three variables. It thus presents an example of a radical equation with three variables and shows a step-by-step process of simplifying it. The steps involve the analysis of the variables and numbers under the radical equation and application of algebraic multiplication of power rules to simplify the equation into a simple equation.
The most crucial piece of information obtained from the video is that the simplification of radical equations involves not only the simplification of variables but also the integers. For instance, in equation 3 √( 27 a 2 b 5 c 3 ), the radical equation has the integer 27 and three variables with various powers. The radical sign requires one to find the cube root of the integer and the variable. However, the integer can be factorized and expressed in a perfect square 3 3 . Also, one can express the bigger powers like five into multiples of a perfect and imperfect square.
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Although the video is precise in explaining how to simplify radical equations of three variables, the introduction part would have been done better. Sal Khan and Monterey Institute for Technology and Education (2011) in the video, goes directly to stating the given example. Then, the video offers an explanation of how to simplify the equation. A better way was to offer little background information on radical equations, the forms in which they are presented, and the steps involved in simplifying them. As such the video would have mentioned that three variable equations are equation that have three unknowns under the radical sign. They occur in various forms that include an expression in form of an equation or ‘’a part of an equation as the provided example. Then the video would have stated that the steps of simplifying the radical equation involve isolation of radicals and expressing them in their least form possible. Therefore for the given example one has to find the perfect squares for a cube root and express higher powers of the variables as factors of a perfect square of a a cube However,
In conclusion, the video’s presents a good explanation on the simplification of three variables radicals. However, the introduction can be improved to enable one to understand how to simplify three-variable radical equations. As such, when presented with radical equations, one is keen to analyze whether the integers and higher power variables can be expressed as perfect squares for easy simplification.
References
Sal Khan and Monterey Institute for Technology and Education. (2011). Simplifying radical expressions: three variables [video]. Retrieved from https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/miscellaneous-radicals/v/simplifying-cube-roots
