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

√2 x √3

  1. √6

  2. √5

  3. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The product of two square roots is the square root of the product: sqrt(a) * sqrt(b) = sqrt(a * b). Thus, sqrt(2) * sqrt(3) = sqrt(6).

Multiple choice

evaluate √-16

  1. 4

  2. 2

  3. 8

  4. no real answer
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The square root of a negative number is not a real number, as no real number squared results in a negative value.

Multiple choice

evaluate √144

  1. 12

  2. 72

  3. 6

  4. 288
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The square root of 144 is the number that, when multiplied by itself, equals 144. Since 12 * 12 = 144, the answer is 12.

Multiple choice

Which of the following could be simplified?

  1. √45

  2. √55

  3. √41

  4. √34
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A square root can be simplified if the number under the radical has a square factor. 45 = 9 * 5, and 9 is a square number, so √45 = 3√5.

Multiple choice

3√2 + 2√3

  1. cannot be added as √3 ≠ √2

  2. 6√6

  3. 5√5

  4. cannot be added as 3 ≠ 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Radicals can only be added if they have the same radicand (the number inside the root). Since √2 and √3 are different, they cannot be combined.

Multiple choice

2√2 + 5√2 =

  1. 7√2

  2. 10√2

  3. 25√2

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

Since both terms contain √2, they are like radicals. Add the coefficients: 2 + 5 = 7, resulting in 7√2.

Multiple choice

Which of the following is equal to √80 ?

  1. √16 × √5 = 4√5

  2. √16 + √5

  3. 8 × √10

  4. √20 + √4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To simplify √80, find the largest square factor. 80 = 16 * 5. Thus, √80 = √16 * √5 = 4√5.

Multiple choice

√50 simplifies to 5√2 because

  1. √5 × √5 × √2 = √50

  2. 5 × 2 = 10

  3. 50 is a square number

  4. 2 + 2 + 2 + 2 + 2 = 50
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To simplify √50, factor it into a square and another number: 50 = 25 * 2. Then √50 = √25 * √2 = 5√2. Option A correctly identifies the prime factorization logic.

Multiple choice

√18 equals to

  1. √2 × √9

  2. 2 × √3

  3. √2 + √3

  4. √2 × √3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the property √a * √b = √(a * b), √18 can be split into factors like √9 * √2.

Multiple choice

Which of the following is equal to 2√3 ?

  1. 2 × √3

  2. 2 + √3

  3. √3 × √3

  4. 3 × √2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The expression 2√3 simply means 2 multiplied by √3. This is the definition of the coefficient notation.

Multiple choice

√2 + √2 =

  1. 2√2

  2. 4

  3. √2

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

Treat √2 as a variable (like x). So, x + x = 2x. Therefore, √2 + √2 = 2√2.

Multiple choice

√2 × √2 =

  1. √4

  2. 4

  3. 2√2

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

Using the rule √a * √a = a, √2 * √2 = 2. However, √2 * √2 is also equal to √4, which simplifies to 2. Option A is technically correct as √4 = 2.

Multiple choice

Choose the biggest number: √6, 2√3, √15, 3√2

  1. √6

  2. 2√3

  3. √15

  4. 3√2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Convert all to square roots: sqrt(6) is sqrt(6), 2*sqrt(3) = sqrt(4 * 3) = sqrt(12), sqrt(15) is sqrt(15), and 3*sqrt(2) = sqrt(9 * 2) = sqrt(18). Since 18 is the largest, 3*sqrt(2) is the biggest.

Multiple choice

√81 + √64 =

  1. 12.041595787923

  2. √145

  3. 9+8

  4. 8+7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

√81 + √64 = 9 + 8 = 17. We cannot combine the radicals as √(81+64). Option C correctly shows this as the sum 9+8.