Quantitative Aptitude · Mathematics

Algebraic Simplification

146 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 √150

  1. 5√6

  2. 5√5

  3. 5√6

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

The factors of 150 are 25 * 6. Therefore, sqrt(150) = sqrt(25) * sqrt(6) = 5 * sqrt(6). Note that options A and C are identical.

Multiple choice

Simplify √63

  1. 3√7

  2. 21√3

  3. 7√3

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

The number 63 can be factored into 9 * 7. Thus, sqrt(63) = sqrt(9) * sqrt(7) = 3 * sqrt(7).

Multiple choice

Simplify √80

  1. 2√20

  2. 8√10

  3. 4√5

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

The number 80 can be factored into 16 * 5. Thus, sqrt(80) = sqrt(16) * sqrt(5) = 4 * sqrt(5).

Multiple choice

Simplify √50

  1. 2√5

  2. 5√2

  3. 10√5

  4. 25√2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The number 50 can be factored into 25 * 2. Thus, sqrt(50) = sqrt(25) * sqrt(2) = 5 * sqrt(2).

Multiple choice

Simplify √32 fully

  1. 2√8

  2. 4√2

  3. 5.8

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

The number 32 can be factored into 16 * 2. Thus, sqrt(32) = sqrt(16) * sqrt(2) = 4 * sqrt(2).

Multiple choice

Expand and simplify (1 - √2)2

  1. 3 - √4

  2. -1 - 2√2

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

Expanding (1 - sqrt(2))^2 gives (1 - sqrt(2))(1 - sqrt(2)) = 1 - sqrt(2) - sqrt(2) + (sqrt(2))^2 = 1 - 2*sqrt(2) + 2 = 3 - 2*sqrt(2).

Multiple choice

Expand and simplify (2 + √5)(3 - √5)

  1. 1 + √5

  2. 11 + √5

  3. 1 - √5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Expanding (2 + sqrt(5))(3 - sqrt(5)) using FOIL: 2*3 - 2*sqrt(5) + 3*sqrt(5) - (sqrt(5))^2 = 6 + sqrt(5) - 5 = 1 + sqrt(5).

Multiple choice

Expand and simplify (2 + √3)(1+√3)

  1. 5+3√3

  2. 11 + 3√3

  3. 5 + 2√6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Expand the expression using the FOIL method: (2 * 1) + (2 * sqrt(3)) + (sqrt(3) * 1) + (sqrt(3) * sqrt(3)). This simplifies to 2 + 2*sqrt(3) + sqrt(3) + 3, which combines to 5 + 3*sqrt(3).

Multiple choice

simplify (√3/2)2

  1. √3/4

  2. 3/4

  3. √9/4

  4. 3/2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When squaring a fraction, square both the numerator and the denominator. (sqrt(3))^2 = 3 and 2^2 = 4, resulting in 3/4.

Multiple choice

simplify: √18 + √2

  1. √20

  2. 3√2

  3. 5√3

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

Simplify sqrt(18) = 3*sqrt(2). Then 3*sqrt(2) + sqrt(2) = 4*sqrt(2).

Multiple choice

Simplify: √18

  1. 9√2

  2. 3√3

  3. 3√2

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

sqrt(18) = sqrt(9 * 2) = sqrt(9) * sqrt(2) = 3*sqrt(2).

Multiple choice

Simplify: (√𝒙)2

  1. 𝒙

  2. 𝒙2

  3. 𝒙1/2

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

By definition, the square of a square root of a non-negative number x is x itself: (sqrt(x))^2 = x.

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).