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Surds and Indices Practice Questions Video Lecture | Quantitative Aptitude (Quant) - CAT

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FAQs on Surds and Indices Practice Questions Video Lecture - Quantitative Aptitude (Quant) - CAT

1. What are surds and how are they related to indices?
Ans. Surds are irrational numbers that cannot be expressed as a fraction and have infinite non-recurring decimal places. Indices, also known as exponents, are used to represent repeated multiplication of a number by itself. Surds and indices are related as surds can be expressed using indices, such as √a can be written as a^(1/2).
2. How do you simplify surds?
Ans. To simplify a surd, you need to find the largest perfect square that can be extracted from the surd. Then, you can simplify the surd by taking the square root of that perfect square and placing it outside the square root symbol. The remaining factor inside the square root symbol cannot be simplified further.
3. What are the rules for performing operations with surds?
Ans. The rules for performing operations with surds are as follows: - Addition and subtraction: Surds with the same radicand can be added or subtracted by combining the coefficients. However, surds with different radicands cannot be combined. - Multiplication: Surds can be multiplied together by multiplying the coefficients and simplifying any common factors. - Division: Surds can be divided by rationalizing the denominator. This involves multiplying both the numerator and denominator by the conjugate of the denominator to eliminate the surd in the denominator.
4. How do you solve equations involving surds?
Ans. To solve equations involving surds, you can follow these steps: 1. Isolate the surd term on one side of the equation. 2. Square both sides of the equation to eliminate the surd. 3. Solve the resulting equation. 4. Check if the obtained solution satisfies the original equation. If it does, it is a valid solution. If not, discard it.
5. Can surds be negative?
Ans. Yes, surds can be negative. Surds can have a positive or negative value depending on the context of the problem. For example, √9 is both +3 and -3. However, when simplifying surds, we usually consider the positive value as the principal square root.
185 videos|158 docs|113 tests
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