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

4√2 + 6√2

  1. 24√2

  2. 10√2

  3. 10√4

  4. 24√3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When adding radicals with the same radicand, add the coefficients: 4*sqrt(2) + 6*sqrt(2) = (4 + 6)*sqrt(2) = 10*sqrt(2).

Multiple choice

6-3

  1. 1/6

  2. 3√6

  3. 1/216
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A negative exponent indicates a reciprocal: 6^(-3) = 1 / 6^3 = 1 / 216.

Multiple choice

√30 + √6

  1. √30 + √6

  2. √36

  3. 6

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

Radicals cannot be added unless the radicands are identical. Since 30 and 6 are different, the expression cannot be simplified further.

Multiple choice

√100 - √81

  1. √1

  2. √19

  3. 4

  4. 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The square root of 100 is 10, and the square root of 81 is 9. Subtracting these results, 10 - 9 = 1.

Multiple choice

√25 + √9

  1. √25 + √9

  2. √34

  3. 8

  4. 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The square root of 25 is 5, and the square root of 9 is 3. Adding these results, 5 + 3 = 8.

Multiple choice

√18 ÷ √9

  1. 1

  2. √2

  3. √9

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

Using the quotient property of radicals, sqrt(a) / sqrt(b) = sqrt(a/b). Thus, sqrt(18) / sqrt(9) = sqrt(18/9) = sqrt(2).

Multiple choice

√30 ÷ √5

  1. √6

  2. 30

  3. √150

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

Using the quotient property of radicals, sqrt(30) / sqrt(5) = sqrt(30/5) = sqrt(6).

Multiple choice

√20 ÷ √5

  1. √4

  2. √100

  3. 2

  4. 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the quotient property of radicals, sqrt(20) / sqrt(5) = sqrt(20/5) = sqrt(4). Since sqrt(4) = 2, the answer is 2.

Multiple choice

√12 ÷ √2

  1. √12 ÷ √2

  2. √6

  3. 6

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

Using the quotient property of radicals, sqrt(12) / sqrt(2) = sqrt(12/2) = sqrt(6).

Multiple choice

√27 ÷ √3

  1. √81

  2. √9

  3. 3

  4. 9
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the quotient property of radicals, sqrt(27) / sqrt(3) = sqrt(27/3) = sqrt(9). Since sqrt(9) = 3, the answer is 3.

Multiple choice

√8 ÷ √2

  1. √4

  2. 2

  3. √16

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

Using the quotient property of radicals, sqrt(8) / sqrt(2) = sqrt(8/2) = sqrt(4). Since sqrt(4) = 2, the answer is 2.

Multiple choice

√12 x √11

  1. √144

  2. √132

  3. 12

  4. 11
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the product property of radicals, sqrt(a) * sqrt(b) = sqrt(a*b). Thus, sqrt(12) * sqrt(11) = sqrt(132).

Multiple choice

√6 x √8

  1. √48

  2. √52

  3. 48

  4. 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the product property of radicals, sqrt(6) * sqrt(8) = sqrt(48).

Multiple choice

√8 x √10

  1. √81

  2. 9

  3. √80

  4. 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the product property of radicals, sqrt(8) * sqrt(10) = sqrt(80).

Multiple choice

√7 x √5

  1. √35

  2. √20

  3. 35

  4. 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the product property of radicals, sqrt(7) * sqrt(5) = sqrt(35).