Quant Booster Dose – Power, Indices, and Surds Questions PDF
Power, Indices, and Surds Questions & Formulas PDF with Answers for government exams like SSC, Railways, Banking, FCI, CWC, Insurance Exams, UPSC, and other state PCS exams. As we all know in many competitive exams in Quantitative Aptitude/ Numerical Ability subject Power, Indices, and Surds Questions asked repeatedly, so you cannot ignore the Power, Indices, and Surds Questions PDF.
As questions are based on previous year papers, there are chances that candidates will find many questions from the Power, Indices, and Surds Questions with Answers PDF in all competitive Exams. If you check the last 4-5 year’s papers of SSC, Railways and Banking Exams, you will find that many different types of Power, Indices, and Surds questions are asked. Today we have compiled “350+ Power, Indices, and Surds Questions PDF with Answers for SSC, Railway & Banking Exam”. You can download Free Power, Indices, and Surds Questions with Solution so that you get all the important questions at one place. And it will become very easy for you guys to revise them.
Power, Indices, and Surds Questions PDF for SSC, Railways and Banking Exams
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Power, Indices, and Surds Questions with Answers | Download Free PDF
What is Power, Indices, and Surds?
Surds are the square roots (√) of numbers that cannot be simplified into a whole or rational number. It cannot be accurately represented in a fraction. In other words, a surd is a root of the whole number that has an irrational value. Consider an example, √2 ≈ 1.414213. It is more accurate if we leave it as a surd √2.
The different types of surds are as follows:
- Simple Surds – A surd that has only one term is called a simple surd. Example: √2, √5, …
- Pure Surds – Surds which are completely irrational. Example: √3
- Similar Surds – The surds having the same common surds factor
- Mixed Surds – Surds that are not completely irrational and can be expressed as a product of a rational number and an irrational number
- Compound Surds – An expression which is the addition or subtraction of two or more surds
- Binomial Surds – A surd that is made of two other surds
Surds are the root values that cannot be written as whole numbers. Indices are the power or exponent of a value. For example, for 32, 2 is the index and 3 is the base.
Suppose, we have a value √33. This value can be written as:
√33 = (33)½ = 33/2
Where 3/2 is the index
Power, Indices, and Surds Formulas
Now that you know the squares and cubes, you are ready to learn the formulae of Surds and Indices for Bank Exams. Here are the formulae to solve all problems related to Surds and Indices for Bank Exams. Memorize each formula and apply them carefully while solving the problems.
Formulae of Indices:
- am x an = am + n
- am / an = am – n
- (am)n = amn
- (ab)n = anbn
- a0 = 1
- (a /b)n = an / bn
Formulae of Surds:
In addition to the formulae, you must also know the identities so that you can find the answers to all problems of Surds and Indices for bank exams:
- (a + b)2 = a2 + 2ab + b2
- (a – b)2 = a2 – 2ab + b2
- a2 – b2= (a + b)(a – b)
- (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
- (a + b)3 = a3 + 3a2b + 3ab2 + b3
- (a – b)3 = a3 – 3a2b + 3ab2– b3
- (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
- (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
Surds and Indices Rules
2√2, where 2 is a rational number and √2 is a surd. Here x, y used in the rules are decimal numbers as follows.
Rules of Surds:
| S. No. | Rules for surds | Example |
|---|---|---|
| 1. | n √x = x1/n | √2 = 21/2 |
| 2. | n√(x ×y) =n √x × n √x | √(2×3)= √2 × √3 |
| 3. | n√(x ÷y)=n √x ÷ n √y | 3√(5÷3) = 3√5 ÷ 3√3 |
| 4. | (n √x)n = x | (√2)2 = 2 |
| 5. | (n√ x)m = n√(x m) | (3√27)2 = 3√(272) = 9 |
| 6. | m√(n√ x) = m × n √x | 2√(3√729)= 2×3√729 = 6√729 = 3 |
Rules of Indices:
| S. No. | Rules for indices | Example |
|---|---|---|
| 1. | x0 = 1 | 20 = 1 |
| 2 | x m × x n = x m +n | 22 ×23= 25 = 32 |
| 3 | x m ÷ x n = x m-n | 23 ÷ 22 = 23-2 = 2 |
| 4 | (x m)n = x m ×n | (23)2 = 23×2 = 64 |
| 5 | (x × y)n = x n × y n | (2 × 3)2= 22 × 32 =36 |
| 6 | (x ÷ y)n = x n ÷ y n | (4 ÷ 2) 2= 42 ÷ 22 = 4 |
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- All the questions prepare by Exams experts.
- The practice questions covered are across the levels i.e. Easy, Moderate, and Difficult.
- Provides a detailed approach to the solution of each question.
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- Power, Indices, and Surds Questions PDF boosts confidence and reduces pre-exam jitters by regularly attempting a variety of questions and tackling the difficulty level expected in the final exam.
This Quant Booster Dose Power, Indices, and Surds Questions PDF is useful for the upcoming Banking and Insurance exams i.e. IBPS PO, SBI PO, Clerk, IBPS RRB PO & Clerk, RBI Assistant, RBI Grade B, NABARD, LIC AAO, SSC (CGL, CHSL, MTS, CPO, and Constable), Railway RRB (NTPC, Group D, JE, ALP) & Other Government Exams.
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