EXERCISES:
1. Read the following words paying attention to the pronunciation:
inverse, perfect, opposite, square, arithmetic, therefore, equality, cube root.
Give English equivalents of the following:
умножить число на себя, точность извлеченного корня, целое число, процесс нахождения корня, проверить количество, под знаком корня, буква, расположенная вверху справа, следует различать, найден правильно.
3. Form Participles using the following verbs:
to square, to use, to raise, to multiply, to find, to check, to give, to begin, to obtain, to get, to take, to be.
4. Make up sentences of your own using the words and expressions given below:
to raise to a power, to obtain the quantity, to square the number, to take an arithmetic square root, may be checked, conclude.
5. Translate into Russian:
Tables of squares are used by architects and engineers in working with squares of a number. If you have a table of squares, you can find the approximate square root of any number. Sometimes it is not easy to find a square root by inspection. If a table of squares is not at hand another method may be used.
6. Answer the following questions:
1. How can you square a number?
2. What does the process of finding the square root mean?
3. The process of finding the square root is called the evolution, isn't it?
4. What is the inverse of evolution?
5. How may the accuracy of the root be checked?
6. What is called the index?
7. Read and translate the text.
Involution
The process of finding any required power of an expression is called involution.
The law of signs for involution is that all powers of a positive number are positive; even powers of a negative number are positive, and odd powers are negative.
To raise an integral term to any power: raise the numerical coefficient to the required power and annex to it each letter with an exponent equal to the product of its exponent by the exponent of the required power; use the law of signs.
To raise a fraction to any power: raise both numerator and denominator to the required power and prefix the proper sign to the result.
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