wishmaster said:Im just wondering what is the easiest way to deal with calculations where roots are involved?
For example how do you solve this one?
\(\displaystyle \frac{\frac{1}{2}}{1-\frac{\sqrt{2}}{2}}\)Thank you for replies!
Prove It said:A rule of thumb for fractions is to get a common denominator and to always attempt to rationalise denominators.
What have you tried so far?
wishmaster said:To multiply the fraction with 2.
MarkFL said:I assume you mean to multiply by:
\(\displaystyle 1=\frac{2}{2}\)
This is a good first step. :D What did you get in doing so?
wishmaster said:Yes,Mark,i did it so as you said. Actualy i understand this,but i am wondering if there some other way to deal with this...
And i got:
\(\displaystyle \frac{1}{2-\sqrt{2}}\)
MarkFL said:Okay, now you want to rationalize the denominator. Think of the difference of squares formula...
wishmaster said:I multiply fraction with \(\displaystyle (2+\sqrt{2})\)
So i got:
\(\displaystyle \frac{2+\sqrt{2}}{2}\)
thank you!MarkFL said:Good! You could choose to leave it like that, or express it as:
\(\displaystyle 1+\frac{\sqrt{2}}{2}\)
A root calculation is a mathematical process used to find the value of a number that, when multiplied by itself a certain number of times, equals a given number. It is also known as finding the "square root" of a number.
The easiest way to solve a root calculation is by using a calculator. Most calculators have a square root function that can quickly and accurately find the value of a root. You can also use a table of square roots or estimation techniques for simpler calculations.
A square root is the value of a number that, when multiplied by itself, equals the given number. A cube root is the value of a number that, when multiplied by itself three times, equals the given number. In other words, a square root is finding the "root" of a number, while a cube root is finding the "third root" of a number.
To check if your root calculation is correct, you can square the value you found using the root calculation. The result should be equal to the original number. For example, if you found the square root of 25 to be 5, you can check by squaring 5, which equals 25.
Yes, you can simplify a root calculation by breaking down the given number into its prime factors. Then, you can take out any pairs of factors and write them as a single factor inside the root. For example, the square root of 72 can be simplified to the square root of 36 x 2, which can then be written as 6√2.