In this set of Math Tutorials we cover Powers and Roots in detail with clear guides, Powers and Roots formulas and working examples. Each tutorial includes example questions, a revision guide and supporting Powers and Roots calculators.
We also provide online Powers and Roots Calculators which allow you to calculate specific Powers and Roots formula in support of the tutorials or to check and verify your own calculations in support of your Powers and Roots homework, math coursework or to help you improve your own understanding so it is easier to teach your children Powers and Roots.
|7.5||Rationalising the Denominator|
This chapter is about indices (otherwise known as exponents) and roots. The first tutorial begins with the definition of indices; then it continues with the properties of indices; then the meaning of reciprocal of a number is given associated with the use of reciprocal in indices. The tutorial then continues with negative indices and the calculation of negative powers, by pointing out the difference between raising negative numbers in odd and even powers.
The second tutorial of this chapter explains roots. It begins with the definition of roots and the geometrical meaning of square and cube roots. Then, it follows with the presentation of roots as fractional powers and the properties of roots. A short description of the meaning of absolute value and the method used to calculate manually the square root of a number, are among other things explained in the rest of this tutorial.
The third tutorial is about standard form (otherwise known as 'scientific notation') - a method used especially for writing very small or very large numbers. The explanation of the standard method is made in combination with the introduction of two other methods of expressing numbers, such as the ordinary and decomposed form. Moreover, in the explanation are not only integers included, but also decimals and other types of numbers.
Another important element discussed in the third tutorial is operations with numbers written in standard form. Again, the explanation is combined with the other two forms of numbers representation. As for multiplication and division, they are explained only in standard form, as the use of the other two methods would result very long. At the end of the tutorial, we look at very big and very small numbers, as well as the powers of numbers written in standard mode is presented.
The fourth tutorial of this chapter is about surds - a name used to describe numbers left inside the roots after making all possible operations and simplifications. First, the difference between surds, irrational and transcendental numbers is highlighted through definitions; then, all types of surds are explained associated with examples. The tutorial follows with the properties of surds and ends with the explanation of methods used to make basic operations with surds.
The fifth and last tutorial of this chapter deals with fractions; more specifically with the rationalization of denominator - an extension of the concept of fractions to also include surds.
The following Math Calculators are provided in support of the Powers and Roots tutorials.