UPSC  >  Problem Set 2 (Surds and Indices) - Quantitative Aptitude

# Problem Set 2 (Surds and Indices) - Quantitative Aptitude Video Lecture - CSAT Preparation - UPSC

## CSAT Preparation

197 videos|151 docs|200 tests

## FAQs on Problem Set 2 (Surds and Indices) - Quantitative Aptitude Video Lecture - CSAT Preparation - UPSC

 1. What are surds and how are they used in mathematics?
Ans. Surds are irrational numbers that cannot be expressed as a simple fraction or a decimal. They are often represented by the symbol √. In mathematics, surds are used to represent the square roots of non-perfect square numbers or any other roots of non-perfect nth power numbers.
 2. How do we simplify surds?
Ans. To simplify surds, we follow certain rules. For example, if we have a surd like √12, we can simplify it by finding the largest perfect square that divides 12 evenly. In this case, it is √4, which simplifies to 2. So, √12 can be simplified to 2√3.
 3. What are indices and how are they used in mathematics?
Ans. Indices, also known as exponents or powers, are used to represent repeated multiplication of the same number. They are written as a small number raised to the right and above the base number. For example, in 2³, the base is 2 and the index is 3. It means 2 multiplied by itself three times (2 x 2 x 2 = 8).
 4. How do we simplify expressions with indices?
Ans. To simplify expressions with indices, we use certain rules. For example, when multiplying two numbers with the same base but different indices, we can add the indices. So, 2² x 2³ can be simplified to 2^(2+3) = 2^5 = 32. Similarly, when dividing two numbers with the same base but different indices, we can subtract the indices.
 5. How are surds and indices used together in mathematics?
Ans. Surds and indices are often used together to solve complex mathematical problems. For example, when simplifying expressions with surds involving indices, we can apply the rules of indices to simplify the expression further. Similarly, when finding the square root or any other root of an expression with indices, we can apply the rules of surds to simplify the answer.

## CSAT Preparation

197 videos|151 docs|200 tests

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