Mathematics · Quantitative Aptitude

Surds and Indices

408 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

What is the rule for finding the cube root of a number according to Virasena?

  1. $$\sqrt[3]{a} = \frac{a}{3}$$
  2. $$\sqrt[3]{a} = \frac{a}{9}$$
  3. $$\sqrt[3]{a} = \frac{a}{27}$$
  4. $$\sqrt[3]{a} = \frac{a}{81}$$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to Virasena, the rule for finding the cube root of a number is $$\sqrt[3]{a} = \frac{a}{27}$$

Multiple choice

What is the name of the mathematical operation that is the inverse of taking the square root?

  1. Squaring

  2. Cubing

  3. Taking the fourth root

  4. Taking the fifth root

  5. Taking the sixth root
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Squaring is the mathematical operation that is the inverse of taking the square root. When you take the square root of a number, you are finding out what number you need to multiply by itself to get the given number. When you square a number, you are multiplying it by itself.

Multiple choice

What was the Babylonian method for calculating square roots?

  1. The Babylonian Method

  2. The Square Root Formula

  3. The Completing the Square Method

  4. The Factoring Method
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Babylonians had a method for calculating square roots that involved using a series of approximations to find the solution.

Multiple choice

Find the square root of 144 using the Dhruva Bheda Sutra.

  1. 11

  2. 13

  3. 12

  4. 14
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The Dhruva Bheda Sutra states that the square root of a number can be found by subtracting the difference between the number and the nearest perfect square from the nearest perfect square. In this case, the nearest perfect square to 144 is 121, and the difference between 144 and 121 is 23. Subtracting 23 from 121 gives us 12, which is the square root of 144.

Multiple choice

Find the square root of 256 using the Panchajanya Sutra.

  1. 16

  2. 18

  3. 14

  4. 12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Panchajanya Sutra states that the square root of a number can be found by dividing the number by 2 and then adding 1 to the result. In this case, 256 / 2 = 128 and 128 + 1 = 129. Therefore, the square root of 256 is 16.

Multiple choice

Find the square root of 625 using the Dhruva Bheda Sutra.

  1. 26

  2. 24

  3. 28

  4. 22
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

The Dhruva Bheda Sutra states that the square root of a number can be found by subtracting the difference between the number and the nearest perfect square from the nearest perfect square. In this case, the nearest perfect square to 625 is 625, and the difference between 625 and 625 is 0. Subtracting 0 from 625 gives us 625, which is the square root of 625.

Multiple choice

Find the square root of 400 using the Panchajanya Sutra.

  1. 21

  2. 20

  3. 18

  4. 16
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The Panchajanya Sutra states that the square root of a number can be found by dividing the number by 2 and then adding 1 to the result. In this case, 400 / 2 = 200 and 200 + 1 = 201. Therefore, the square root of 400 is 20.

Multiple choice

What is the value of (-3)^3?

  1. -9

  2. -27

  3. -81

  4. -243
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

(-3)^3 means -3 raised to the power of 3. This is calculated as -3 × -3 × -3, which equals -27.

Multiple choice

What is the formula for calculating root mean squared error?

  1. Root mean squared error = √sqrt((1/n) * Σ(y_i - μ_i)^2)

  2. Root mean squared error = √sqrt((1/n) * Σ(y_i - μ_i))

  3. Root mean squared error = √sqrt(Σ(y_i - μ_i)^2)

  4. Root mean squared error = √sqrt(Σ(y_i - μ_i))
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Root mean squared error is calculated by taking the square root of the mean squared error.

Multiple choice

Evaluate the expression: ( \sqrt{16} )

  1. \( 2 \)
  2. \( 4 \)
  3. \( 8 \)
  4. \( 16 \)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The square root of a number is the value that, when multiplied by itself, gives the original number. Therefore, ( \sqrt{16} = 4 ), since ( 4 \cdot 4 = 16 ).

Multiple choice

Find the value of ( \sqrt[3]{8} )

  1. \( 2 \)
  2. \( 3 \)
  3. \( 4 \)
  4. \( 6 \)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The cube root of a number is the value that, when multiplied by itself three times, gives the original number. Therefore, ( \sqrt[3]{8} = 2 ), since ( 2 \cdot 2 \cdot 2 = 8 ).

Multiple choice

Find the value of ( \sqrt[4]{625} )

  1. \( 5 \)
  2. \( 10 \)
  3. \( 15 \)
  4. \( 20 \)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The fourth root of a number is the value that, when multiplied by itself four times, gives the original number. Therefore, ( \sqrt[4]{625} = 5 ), since ( 5 \cdot 5 \cdot 5 \cdot 5 = 625 ).

Multiple choice

Find the value of ( \sqrt[5]{32} )

  1. \( 2 \)
  2. \( 4 \)
  3. \( 6 \)
  4. \( 8 \)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The fifth root of a number is the value that, when multiplied by itself five times, gives the original number. Therefore, ( \sqrt[5]{32} = 2 ), since ( 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 32 ).

Multiple choice

Evaluate the expression: ( \sqrt{144} - \sqrt{36} )

  1. \( 4 \)
  2. \( 6 \)
  3. \( 8 \)
  4. \( 10 \)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simplifying the expression, we have ( \sqrt{144} - \sqrt{36} = 12 - 6 = 6 ).

Multiple choice

Find the characteristic of the field GF(2^8).

  1. 2

  2. 4

  3. 8

  4. 16
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The characteristic of a field is the smallest positive integer n such that 1 + 1 + ... + 1 (n times) = 0. In the field GF(2^8), the smallest positive integer n such that 1 + 1 + ... + 1 (n times) = 0 is 2. Therefore, the characteristic of the field GF(2^8) is 2.