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

Square root of 54/9 equals

  1. √5 + 2/3

  2. 21/3

  3. 22/3

  4. 71/3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

sqrt(5 4/9) = sqrt(49/9). The square root of 49/9 is 7/3, which equals 2 1/3.

Multiple choice

(3√5)2

  1. 45

  2. 30

  3. 15

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

(3*sqrt(5))^2 = 3^2 * (sqrt(5))^2 = 9 * 5 = 45.

Multiple choice

(√6)2

  1. 2

  2. √36

  3. √12

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

(sqrt(6))^2 = 6 by definition of the square root.

Multiple choice

5√3*8√5

  1. 13√15

  2. 40√15

  3. 13√3

  4. 5√15
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

5*sqrt(3) * 8*sqrt(5) = (5 * 8) * sqrt(3 * 5) = 40*sqrt(15).

Multiple choice

√11*√7

  1. √18

  2. √77

  3. √11

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

sqrt(11) * sqrt(7) = sqrt(11 * 7) = sqrt(77).

Multiple choice

√384

  1. 384

  2. 6√6

  3. 64

  4. 8√6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

sqrt(384) = sqrt(64 * 6) = 8*sqrt(6).

Multiple choice

√6+√6

  1. √12

  2. √36

  3. 2√6

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

sqrt(6) + sqrt(6) = 2*sqrt(6).

Multiple choice

√16

  1. 4

  2. 16

  3. 2

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

The square root of 16 is 4.

Multiple choice

4√15 x 2√18

  1. 8√270

  2. 6√270

  3. 72√30

  4. 24√30
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Multiply the coefficients (4 * 2 = 8) and the radicands (sqrt(15) * sqrt(18) = sqrt(270)). Simplify sqrt(270) = sqrt(9 * 30) = 3 * sqrt(30). Thus, 8 * 3 * sqrt(30) = 24 * sqrt(30).

Multiple choice

√3 (√2 - √5)

  1. √5 - √8

  2. √6 - √15

  3. -9

  4. √6 + √15
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distribute the sqrt(3) to both terms inside the parentheses: sqrt(3) * sqrt(2) = sqrt(6) and sqrt(3) * sqrt(5) = sqrt(15). The expression becomes sqrt(6) - sqrt(15).

Multiple choice

√50 - √8

  1. 3√2

  2. 5√4

  3. 7√2

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

Simplify the radicals first: sqrt(50) = sqrt(25 * 2) = 5 * sqrt(2) and sqrt(8) = sqrt(4 * 2) = 2 * sqrt(2). Then, 5 * sqrt(2) - 2 * sqrt(2) = 3 * sqrt(2).

Multiple choice

(-5√10 ÷ 6) + (3√10 ÷ 8)

  1. -100√3 ÷ 4

  2. -11√5 ÷ 24

  3. -11√10 ÷ 24

  4. -11√10 ÷ 12
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Find a common denominator for the fractions 6 and 8, which is 24. The expression becomes (-20 * sqrt(10) / 24) + (9 * sqrt(10) / 24) = -11 * sqrt(10) / 24.