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

√3 x √5

  1. √3

  2. 3

  3. 6

  4. √15
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the product property of radicals, sqrt(3) * sqrt(5) = sqrt(15).

Multiple choice

√2 x √5

  1. 10

  2. √10

  3. 5

  4. √8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the product property of radicals, sqrt(2) * sqrt(5) = sqrt(10).

Multiple choice

√16 x √4

  1. 8

  2. √64

  3. √8

  4. 64
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The square root of 16 is 4, and the square root of 4 is 2. Multiplying these results, 4 * 2 = 8.

Multiple choice

√3 x √12

  1. 6

  2. √36

  3. √6

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

Using the product property of radicals, sqrt(3) * sqrt(12) = sqrt(36). Since sqrt(36) = 6, the answer is 6.

Multiple choice

√5 x √20

  1. √10

  2. 5

  3. √100

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

Using the product property of radicals, sqrt(5) * sqrt(20) = sqrt(100). Since sqrt(100) = 10, the answer is 10.

Multiple choice

√2 x √8

  1. √16

  2. 4

  3. 16

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

Using the product property of radicals, sqrt(2) * sqrt(8) = sqrt(16). Since sqrt(16) = 4, the answer is 4.

Multiple choice

√20 + √180 - √125

  1. √75

  2. 3√5

  3. 3√15
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Simplify each radical: sqrt(20) = 2*sqrt(5), sqrt(180) = 6*sqrt(5), and sqrt(125) = 5*sqrt(5). Combining these gives 2*sqrt(5) + 6*sqrt(5) - 5*sqrt(5) = 3*sqrt(5).

Multiple choice

√48 - √12

  1. 2

  2. √36

  3. 2√3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simplify the radicals: sqrt(48) = sqrt(16 * 3) = 4*sqrt(3) and sqrt(12) = sqrt(4 * 3) = 2*sqrt(3). Subtracting them gives 4*sqrt(3) - 2*sqrt(3) = 2*sqrt(3).

Multiple choice

√18 + √8

  1. 5√2

  2. √26

  3. 6√2

  4. 5√4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simplify the radicals: sqrt(18) = 3*sqrt(2) and sqrt(8) = 2*sqrt(2). Adding them gives 3*sqrt(2) + 2*sqrt(2) = 5*sqrt(2).

Multiple choice

4√2 x √3 ÷ 2√2

  1. 6

  2. 2√3

  3. 8√7

  4. 16√3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The expression is (4*sqrt(2) * sqrt(3)) / (2*sqrt(2)). Cancel the common factor sqrt(2) to get (4 * sqrt(3)) / 2, which simplifies to 2*sqrt(3).

Multiple choice

12√56 ÷ 6√8

  1. 7√2

  2. 9

  3. 14

  4. 2√7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Divide the coefficients (12 / 6 = 2) and the radicals (sqrt(56) / sqrt(8) = sqrt(56/8) = sqrt(7)). The result is 2*sqrt(7).

Multiple choice

3√15 ÷ √3

  1. 15

  2. √15

  3. 3√5

  4. 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Divide the coefficients (3 / 1 = 3) and the radicals (sqrt(15) / sqrt(3) = sqrt(15/3) = sqrt(5)). The result is 3*sqrt(5).

Multiple choice

√2 x √3 ÷ √2

  1. √2

  2. √3

  3. 3

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The expression is (sqrt(2) * sqrt(3)) / sqrt(2). The sqrt(2) terms cancel out, leaving sqrt(3).

Multiple choice

√12 ÷ √3

  1. 4

  2. √4

  3. √9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

sqrt(12) / sqrt(3) = sqrt(12 / 3) = sqrt(4).