## Important Formulas - Surds and Indices

- An integer is a whole number (positive, negative or zero). A rational number is one that can be expressed as a fraction , where a and b are integers. All integers, fractions and terminating or recurring decimals are rational.
- An irrational number cannot be expressed in the form , where a and b are integers. Examples of irrational numbers are .
- Real numbers are numbers that can be represented by points on the number line. Real numbers include both rational and irrational number.
- A surd is an irrational number involving a root. The numbers are examples of surds. Numbers such as are not surds because they are equal to rational numbers. =4 and root of ‘3’ or ‘root 3’. Note that we cannot take the square root of a negative number.
- Like surds involve the square root of the same number. Only like surds can be added or subtracted. For example, .
- Surds of the form can be simplified if the number beneath the square root sign has a factor that is a perfect square. For example, .

- The following rules can be used when multiplying or dividing surds.

- Rationalising the denominator of a surd means changing the denominator so that is a rational number. To rationalize the denominator of a surd such as we use the result thatso if we multiply the denominator byit will be rational. if we multiply the demoniator bywe must also multiply the numerators byso that
- Fractional indices may be used to express roots.
- Make sure you can use your calculator to find powers and roots. Theor button allows you to find roots.

**For example:**

## INDICES

- When the powers are fraction , then we can compare the indices in following manner.

for example :find which is greather or

step-1 : find the L.C.M of the denominator of the fraction i.e 4,5 = 20

step-2 : find powers with the L.C.M OR = AND

step-3 : compare the result obtained in setp-2 : i.e as 32 < 81 we can say <

## POINT TO REMEMBER

- Any none - zero real number raised to the power 0 equals 1
- I raised to any power is always 1.
- …….m times
- root of
- If a 1; A0; a-1 and , then x = y
- if then
- if x is odd, a=b
- if x is even, a=b

## Important Examples - Surds and Indices

**Question** 1.What is the value of

**Solution**:

The answer is 8+4+2=14

**Question** 2.The product of is equal to

**Solution**:

**Question** 3.The value of is equal to

**Solution**:

=

=

**Question** 4.If x=-5 and y=-6, then what is the value of ?

**Solution**:

**Question** 5.In a cricket match, the number of runs scored by any team is equal to a power of the number of batsman playing in the team. Six batsman played in team A and eleven batsman played in team B. If team A won by 95 runs, then find the run scored by team A.

**Solution**: Let the power of the terms be x and y.

=95

Put x =3, y= 2 (By trial and error)

=95

Hence satisfied

Score of team A= = 216

Note: These type of questions can be solved through answer choices.

**POINTS TO REMEMBER**

- The conjugate surd of
- To rationalize
- If , then a=c and b=d
- To find Write it in the form m+n+, such that m+n=a and 4mn=b, then
- If =p, then p(p-1)=a
- The rationalizing factor of
- The rationalize factor of
- The rationalize factor of
- The rationalize factor of
- The rationalize factor of

## SOLVED EXAMPLES - Surds and Indices

**Question** 1.The value of .

**Solution** : The given expression is in the form of

The exponent i.e., is in form of an infinite G.P

The given expression=

**Question** 2.Simplify

**Solution** :By rationalizing

=

=

**Question** 3.If , then find the value of (a+2b)

**Solution** :

=

=

=

**Question** 4.What is the positive square root of ?

**Solution** :

=

**Question** 5.Which of the following is the great ?

**Solution** :By squaring the values

=

=

Since 25 is common to all the value, is the largest value.

Hence has the largest value.

## Surds and Indices Questions from Previous Year Exams

This test will cover Square, Cube, Indices and Surds syllabus of Bank Clerk Exam.

Dear all, I really do like your little quiz, but unfortunately the answer you are suggesting to question #10 ("Bank PO 1990") is not correct. Instead of 4 - as suggested - the correct answer is 2. (Maybe you forgot to calculate SQRT(4) during simplification 🙂 )

Superb Knowledge is available with you but there are some blunders.Hope you will correct,Thank you so much.

nice pdf

help solve 5+2 root 6 all this into a square root =root2+root3