Look at your root. If the numberrecorded under the root is a perfect square of another number (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ... ), remove the root. That is find such a whole number, the square of which is the numberrecorded under the root. Multiply it by the second multiplier. Write down the answer.
If the square root is not removed, then usually the answer can be recorded by simply removing the multiplication sign. It turns out the numberconsisting of an integer and a nearby root. This will mean that this root is taken such that an integer number of times. A whole number is usually written to the left of the root.
If you want all the number to enter under root, do the following. Construct the whole piece into a square. Comnote on the number, standing under a root. Note the resulting number under the root. This will be your answer.
Square root - a root of degree 2. If the task uses the roots as much as other degrees, change the necessary extent in the solution algorithm.
Recommend you often look in your math textbook. There you will find a lot of useful and valuable information that will surely help you in solving mathematical problems.
Advice 2: How to multiply square root square root
One of the four elementary mathematical operations (multiplication) has created another, somewhat more sophisticated exponentiation. That, in turn, has added additional complexity in the teaching of mathematics, giving rise to reverse a surgery - extraction of root. Any of these operations, you can use any other mathematical operation, which further confuses the study of the subject. To make it all somehow organize, there are sets of rules, one of which reglementary the order of multiplication of the roots.
Use for multiplication of square roots rule, the result should be the square root, radicals which is the product of radical expressions roots of multipliers. This rule applies when multiplying two, three or any other number of square roots. However, it applies not only to the roots of the quadratic, but cubic, or any other exponent, if this figure is the same for all involved in the operation of the radicals.
If the signs multiply roots are numerical values, multiply them together and place the resulting value under the root. For example, when multiplying √3,14 on √a 7.62 this action can be written as: √3,14 * √7,62 = √(3,14*7,62) = √23,9268.
If radical expressions contain variables, we first write the product under the same radical sign, and then try to simplify radical expression is obtained. For example, if it is necessary to multiply √(x+7) √(x-14) operation can be written as: √(x+7) * √(x-14) = √((x+7) * (x-14)) = √(x2-14*x+7*x-7*14) = √(x2-7*x-98).
If you need to multiply more than two square roots act in the same way - gather under one radical sign radical expression multiply all the roots as multipliers of one complex expression, and then simplify it. For example, when multiplying square roots of numbers 3,14, 7,62 and 5,56 can be written as: √3,14 * √7,62 * √5,56 = √(3,14*7,62*5,56) = √133,033008. And the multiplication of the square roots derived from expressions with variables x+7, x-14 and 2*x+1, so: √(x+7) * √(x-14) * √(2*x+1) = √((x+7) * (x-14) * (2*x+1)) = √((x2-14*x+7*x-7*14) * (2*x+1)) = √((x2-7*x-98) * (2*x+1)) = √(2*x*x2-2*x*7*x-2*x*98 + x2-7*x-98) = √(2*x3-14*x2-196*x+x2-7*x-98) = √(2*x3-13*x2-205*x-98).
Advice 3: How to build a root square
The construction of the degree is the abbreviated form of record of the operation of repeated multiplication, in which all multipliers is equal to the original number. And the root means - the definition of the multiplier that should be involved in the operation of multiple multiplication that its result is a radical number. As the exponent and the index of the root point to the same thing - how many factors should be a multiplication operation.
You will need
- Access to the Internet.
If the number or expression you want to apply simultaneously, and the operation of root extraction, and the construction of its degree, bring both actions in a single - exponentiation with a fractional exponent. In the numerator of the fraction must be the exponent, and the denominator the root. For example, if you want to build in the square of cubic root, then the two operations will be equivalent to one construction of the power⅔.
If the conditions required to build in square root with exponent equal to two, this task is not the calculation, and to check your knowledge. Use method from the first step and you will get the fraction 2/2, i.e. 1. This means that the result of raising to the square the squaretion of the square root of any number is the number itself.
If necessary, raised to a square root with an even exponent, it is always possible to simplify the operation. Since the two (the numerator of the fractional exponent) and any even number (the denominator) have a common divisor, then after simplification of the fraction in the numerator will be one and that means to involve in calculations, it is enough to extract the root with half the exponent. For example, in the construction of the square root, the sixth power of eight can be reduced to extracting from it a cube root, because 2/6=1/3.
To calculate the result in all indicators of the degree of root use, for example, a calculator built into the Google search engine. This is perhaps the easiest method of payment you have access to the Internet from your computer. A common substitute symbol for the operation of exponentiation is that such a "lid": ^. Use it when typing in Google search query. For example, if you want to build in square root of the fifth degree from among 750, formulate the query: 750^(2/5). After entering the search without even clicking send to the server will show the result of calculations with the accuracy of seven decimal places: 750^(2 / 5) = 14,1261725.