Mathematics · Quantitative Aptitude

Surds and Indices

362 Questions

Surds and indices questions focus on evaluating square roots, cube roots, and fractional exponents. These topics are a core part of the quantitative aptitude section in many competitive exams. Practicing these problems builds speed and accuracy for solving numerical equations.

Square roots evaluationCube roots calculationExponents and powersFractional exponentsSurds multiplication

Surds and Indices Questions

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

The simplest rationalizing factor of $\sqrt{75}$ is.

  1. $(75)^{1/3}$
  2. $5\sqrt3$
  3. $3$
  4. $\sqrt{150}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let us first factorize $75$ as shown below:


$75=3\times 5\times 5=3\times { 5 }^{ 2 }$

Now consider $\sqrt {75}$ as follows:

$\sqrt { 75 } =\sqrt { 3\times 5\times 5 } =\sqrt { 3\times { 5 }^{ 2 } } =\sqrt { 3 } \times \sqrt { { 5 }^{ 2 } } =5\sqrt { 3 }$

Hence, the simplest rationalizing factor of $\sqrt {75}$ is $5\sqrt { 3 }$.

Multiple choice

What is the value of the square root of 2 according to Vagbhata?

  1. 1.414

  2. 1.4142

  3. 1.41421

  4. 1.414213
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Vagbhata calculated the square root of 2 to five decimal places, which is an impressive achievement for his time.

Multiple choice

The ancient Indian mathematical text, the 'Baudhayana Sulba Sutra', contains a formula for calculating the square root of 2. What is the approximate value of the square root of 2 according to this formula?

  1. 1.4142

  2. 1.4286

  3. 1.4422

  4. 1.4558
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Baudhayana Sulba Sutra provides a formula for calculating the square root of 2, which yields an approximate value of 1.4142, remarkably close to the actual value.

Multiple choice

What does the symbol (\sqrt{}) represent?

  1. Square root

  2. Cube root

  3. Fourth root

  4. Fifth root
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(\sqrt{}) is a mathematical symbol that represents the square root of a number. It is used to find the positive square root of a number.

Multiple choice

What is the formula for finding the square root of a number given by Dandin?

  1. $\sqrt{a} = \frac{a}{2}$
  2. $\sqrt{a} = \frac{a}{4}$
  3. $\sqrt{a} = \frac{a}{8}$
  4. $\sqrt{a} = \frac{a}{16}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Dandin provided a formula for finding the square root of a number, which is (\sqrt{a} = \frac{a}{4}).

Multiple choice

What is the square root of zero?

  1. 0

  2. 1

  3. Undefined

  4. Infinity
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The square root of a number is the number that, when multiplied by itself, results in the original number. The square root of zero is zero because 0 * 0 = 0.

Multiple choice

What is the cube root of zero?

  1. 0

  2. 1

  3. Undefined

  4. Infinity
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The cube root of a number is the number that, when multiplied by itself three times, results in the original number. The cube root of zero is zero because 0 * 0 * 0 = 0.

Multiple choice

What is the fourth root of zero?

  1. 0

  2. 1

  3. Undefined

  4. Infinity
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The fourth root of a number is the number that, when multiplied by itself four times, results in the original number. The fourth root of zero is zero because 0 * 0 * 0 * 0 = 0.

Multiple choice

What is the nth root of zero?

  1. 0

  2. 1

  3. Undefined

  4. Infinity
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The nth root of a number is the number that, when multiplied by itself n times, results in the original number. The nth root of zero is zero for any positive integer n because 0 * 0 * ... * 0 (n times) = 0.

Multiple choice

What is the value of the square root of 144?

  1. 12

  2. 14

  3. 16

  4. 18
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The square root of 144 is 12.

Multiple choice

What is the value of the cube root of 27?

  1. 3

  2. 4

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The cube root of 27 is 3.

Multiple choice

What is the mathematical symbol for the square root in the Indian numeral system?

  1. √

  2. ²

  3. ³

  4. ¼
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In the Indian numeral system, the mathematical symbol for the square root is a small square root sign, similar to the one used in modern mathematics.

Multiple choice

What is the value of the expression sec(π/3)?

  1. 2

  2. √3

  3. 2√3

  4. 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The expression sec(π/3) means the secant of the angle π/3. Since the secant of an angle is the ratio of the hypotenuse to the adjacent side of a right triangle, and the hypotenuse and the adjacent side of a right triangle with an angle of π/3 are equal, the value of the expression is 2.

Multiple choice

What is the value of the expression csc(π/6)?

  1. 2

  2. √3

  3. 2√3

  4. 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The expression csc(π/6) means the cosecant of the angle π/6. Since the cosecant of an angle is the ratio of the hypotenuse to the opposite side of a right triangle, and the hypotenuse and the opposite side of a right triangle with an angle of π/6 are equal, the value of the expression is 2√3.

Multiple choice

What is the value of the expression (2^3)^2?

  1. 32

  2. 64

  3. 128

  4. 256
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The expression (2^3)^2 is equal to 2^(3 * 2) = 2^6 = 64.