Quantitative Aptitude · Mathematics

Algebraic Simplification

151 Questions

Algebraic simplification involves reducing mathematical expressions to their simplest forms using exponent rules and identities. Test takers must manipulate equations to find rapid solutions. This skill is frequently assessed in SSC, banking, and railway quantitative aptitude sections.

Exponent rulesSurd operationsAlgebraic identitiesTrigonometric simplificationLogical expressions

Algebraic Simplification Questions

Multiple choice

Simplify: √5 × √3

  1. √53

  2. √8

  3. √15

  4. √5 × √3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

Multiple choice

simplify: 3√7 − 2√6 + 2√7

  1. 4√13

  2. 4√8

  3. √7 − 2√6

  4. 5√7 − 2√6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Combine like terms: (3*sqrt(7) + 2*sqrt(7)) - 2*sqrt(6) = 5*sqrt(7) - 2*sqrt(6).

Multiple choice

simplify: 11√3 − 4√3

  1. 9√3

  2. 8√3

  3. 7√3

  4. 6√3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To simplify expressions with like radicals, subtract the coefficients while keeping the radical part the same. Here, 11 - 4 = 7, so the result is 7√3.

Multiple choice

simplify: 2√5 + 3√5

  1. 6√5

  2. 5√5

  3. 5√25

  4. 25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Like radicals are added by summing their coefficients. 2 + 3 = 5, resulting in 5√5.

Multiple choice

√28 simplifies to

  1. 2√7

  2. 2√14

  3. 7√2

  4. 8√3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Factor 28 into a square and another number: 28 = 4 * 7. Then √28 = √4 * √7 = 2√7.

Multiple choice

Simplify √24 + √54

  1. 5√6

  2. 13√6

  3. √78

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

Simplify the radicals: sqrt(24) = sqrt(4 * 6) = 2*sqrt(6) and sqrt(54) = sqrt(9 * 6) = 3*sqrt(6). Adding them together: 2*sqrt(6) + 3*sqrt(6) = 5*sqrt(6).

Multiple choice

Simplify -8√2 ÷ 2√26

  1. 4 (√2 ÷ √26)

  2. -4 (√2 ÷ √26)

  3. -4 √ (1÷13)

  4. 4 √ (1÷13)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Divide the coefficients (-8/2 = -4) and the radicals (sqrt(2)/sqrt(26) = sqrt(2/26) = sqrt(1/13)). The result is -4 * sqrt(1/13).

Multiple choice

Simplify (3√147) ÷ 14

  1. (3√3) ÷ 2

  2. (3√3) ÷ 3

  3. (3√3) ÷ 6

  4. (3√3) ÷ 9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simplify sqrt(147) = sqrt(49 * 3) = 7 * sqrt(3). The expression becomes (3 * 7 * sqrt(3)) / 14 = 21 * sqrt(3) / 14. Dividing both by 7 gives (3 * sqrt(3)) / 2.

Multiple choice

Simplify 2√3 + 2√7 + 2√3 - 2√7

  1. 4√7

  2. 4√3 -√7

  3. 2√3 + 2√7

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

Group the like terms: (2 * sqrt(3) + 2 * sqrt(3)) + (2 * sqrt(7) - 2 * sqrt(7)) = 4 * sqrt(3) + 0 = 4 * sqrt(3).

Multiple choice

Simplify √45

  1. 2√5

  2. 3√5

  3. 5√2

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

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