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How do you simplify a radical expression square?

More complex radical square root expressions feature variables represented by letters rather than numbers. The rules for simplifying such expressions are the same as those for simplifying numbers. To simplify the square root of 16y^4, identify that both 16 and y^4 are perfect squares. The square root of 16 is 4, while that of y^4 is y^2. Thus, you can eliminate the radical sign entirely, leaving you with the final answer 4y^2.\nAnother example is the square root of (6x - 16)^4. This problem requires identifying that (6x - 16)^4 is the same thing as (6x - 16) multiplied by itself four times, me..

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What is a comparison theorem?

There are times when it’s not possible to integrate, yet important to examine, the behavior of an integral. For example, if f and g are continuous functions, such that 0 ? g (x) ? f(x) for x ? ?, and function f(x) dx converges, then function g(x) dx converges, and if g(x) dx diverges, then function f(x) dx diverges.

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How do you find diameter?

Understand the meaning of piThe ratio of the circumference of a circle to the diameter is pi. This means for every one unit of the diameter, there are pi units of the circumference. Pi does not have an exact numerical representation, but 3.14 is a close approximation.Divide by piDivide the value of the circle's circumference by pi. This gives the diameter of the circle. Keep your units consistentIf the circumference is given in a specific unit of measurement, such as centimeters, then the diameter is also expressed in the same way. If no unit is given, do not add one to the diameter.

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What is a verbal model in math?

For example, the following is a verbal phrase: "John went to the store and bought five apples. Each apple cost $1.25. How much did John spend before tax?" To translate it to a verbal model, the problem solver represents the problem in simplified words that represent the cost of the apple times the number of apples bought. To translate it further to a mathematical phrase, the problem solver puts numbers in the problem: "$1.25 times 5."

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What is an equation?

In most equations, one or both sides have variables associated with them. The variable represents an unknown number. Manipulating the equation to come up with the solution to the variable is known as "solving the equation." Algebra covers a variety of types of equations and methods to solve them. For example, algebra covers linear equations of one, two or an indefinite number of variables, quadratic equations and equations of higher orders of power.

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What is the prime factorization of 96?

Prime factorization is a process for finding which prime numbers can be multiplied together to make a number; prime numbers are numbers that can only by divided by 1 and themselves. Dividing 96 by the smallest prime number, 2, results in the factor of 48. One can continue this process of dividing 48 by 2 until the only remaining factor is 3, which is also a prime number. At this point the process is done, with the resulting equation of 2 x 2 x 2 x 2 x 2 x 3 = 96.

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How do you calculate your ideal weight?

Women over 5 feet tall multiply the number of inches over 5 feet by five and add it to 100. A woman who is 5 feet, 4 inches tall would multiply four by five and get 20. Her ideal weight is 120 pounds. Women shorter than 5 feet multiply the number of inches below five feet by 5 and subtract the number from 100. A woman who is 4 feet, 9 inches tall multiplies three by five for a product of 15. Her ideal weight is 85 pounds.\nThe same calculations occur for men but there is a different starting height and weight. A man who is 6 feet, 5 inches tall multiplies five by five for a product of 25. His ..

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What are the advantages of probability sampling?

Probability sampling is useful for studying units of both similar and different samples within a group. Random types of probability sampling allow for the elimination of any possible conscious or inherent bias in those conducting the study as the samples are selected at random. Focusing on the features and behavior of the sample in relation to the larger group they are a part of is called statistical inference, and helps generalize the overall behavior of a group. Statistical data on a sample may be collected through direct observation or surveys.\nSimple random and systemic sampling are both ..

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What are some properties of ln x + ln y?

For example, the expression ln(2) + ln(3) uses the product rule to become the ln(2 * 3), which is equal to the ln(6). The quotient rule for natural logarithms is related to the product rule and is used when a natural logarithm is subtracted from another natural logarithm. This rule is expressed as ln(x / y) = ln(x) - ln(y).\nOther rules used to evaluate natural logarithm expressions that include both an x and y variable include the power rule, which is expressed in mathematical notation as ln(x^y) = y ? ln(x). Additional general identities used when evaluating natural logarithms include the de..

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How do you divide numbers?

Identify the dividend and the divisorA division problem has two numbers. The dividend is the number to be divided into. The divisor is the number to be divided by.Divide the first digit of the dividend by the divisorDetermine how many times the entire divisor can be included in the first digit of the dividend. The result is a single-digit number. Note that number on your problem.Multiply that result by the divisorMultiply the result of the previous step by the divisor, and place the product underneath the first digit of the dividend.Subtract that result from the first digit of the dividendStil..

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