write note on concept of surd
fem
Since this is not my area of expertise, I searched Google under the key words "math surd" to get these possible sources:
http://www.google.com/search?client=safari&rls=en&q=math+surd&ie=UTF-8&oe=UTF-8
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
The concept of surd is a fundamental concept in mathematics, specifically in the field of number theory. A surd is an irrational number that cannot be expressed precisely as a fraction, like the square root of a non-perfect square.
To understand the concept of surd, it's important to have some background knowledge about rational and irrational numbers. Rational numbers are those that can be expressed as a fraction, such as 1/2 or 3/4, where the numerator and denominator are both integers. Irrational numbers, on the other hand, cannot be expressed as a fraction and have endless non-repeating decimal representations, such as √2 or π.
Now, let's focus on surds. A surd is a specific type of irrational number that involves the square root (√) or cube root (∛) of a non-perfect square or non-perfect cube. For example, √2 or ∛3 are surds.
To work with surds, it's important to understand a few key properties:
1. Surds cannot be simplified: Unlike rational numbers, surds cannot be simplified to a fraction or a whole number. For example, the square root of 8 (√8) cannot be simplified because 8 is not a perfect square.
2. Surds can be represented as irrational numbers: Since surds are a type of irrational number, they can be represented using decimal notation. However, these decimal representations are non-terminating and non-repeating.
3. Surds can be operated upon: Surds can be added, subtracted, multiplied, and divided, just like other numbers. However, in some cases, the result may still be a surd or an irrational number.
4. Surds can be rationalized: Sometimes, it is useful to rationalize surds to eliminate the radical sign (√) in the denominator. This is done by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of a surd is the same expression but with the opposite sign. This process results in a rational number or a new surd with a simplified form.
So, in summary, surds are a type of irrational number involving the square root or cube root of non-perfect squares or cubes. They cannot be expressed as fractions and have non-repeating, non-terminating decimal representations. Surds can be manipulated using normal arithmetic operations and can be rationalized to simplify expressions involving them.