Rules of Surds

Some of the important rules of surds are listed below.

1. Every rational number is not a surd.

2. Every irrational number is a surd.

3. A root of a positive real quantity is called a surd if its value cannot he exactly determined.

√9, βˆ›64, ∜(16/81) etc. are rational numbers but not surds because √9 = 3, βˆ›64 = 4, ∜(16/81) = 2/3 etc.

4. βˆša Γ— √a = a β‡’ √5 Γ— √5 = 5

5. The sum and difference of two simple quadratic surds are said to be conjugate surds or complementary surds to each other. Thus, (4√7 + √6) and (4√7 - √6) are surds conjugate to each other.

6. To express in the simplest form, denominator must be rationalized.

7. The method of convening a given surd into a rational number on multiplication by another suitable surd is called rationalization of surds. In this case the multiplying surd is called the rationalizing factor of the given surd and conversely.

8. If a and b are both rationals and √x and √y are both surds and a + √x = b + √y then a = b and x = y

9. If a - √x = b - √y then a = b and x = y.

10.  If a + √x = 0, then a = 0 and x = 0.

11. If a - √x = 0, then a = 0 and x = 0.





11 and 12 Grade Math

From Rules of Surds to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 25, 25 12:21 PM

    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  2. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  3. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  4. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

    Jul 23, 25 11:37 AM

    Volume of a Cube
    A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

    Read More

  5. 5th Grade Volume | Units of Volume | Measurement of Volume|Cubic Units

    Jul 20, 25 10:22 AM

    Cubes in Cuboid
    Volume is the amount of space enclosed by an object or shape, how much 3-dimensional space (length, height, and width) it occupies. A flat shape like triangle, square and rectangle occupies surface on…

    Read More