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: 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).

Multiple choice maths square root square root of perfect square finding square root of a number square root of a perfect square

Simplify the expression involving rational exponents:
${ \left( \displaystyle\frac { 25 }{ 64 }  \right)  }^{ { 1 }/{ 2 } }$

  1. $\displaystyle\frac { 25 }{ 8 } $

  2. Not a real number
  3. $\displaystyle\frac { 5 }{ 8 } $
  4. $\displaystyle\frac { 5 }{ 64 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\left(\dfrac{25}{64}\right)^\frac{1}{2}$ = $\left(\dfrac{5^2}{8^2}\right)^\frac{1}{2}$ = $\dfrac{5}{8}$

Multiple choice maths power and exponent power of powers laws of exponents and powers law of indices

Simplify: $( 16x ^{16} )^{\dfrac{3}{4}}$

  1. $8 x^{16}$
  2. $2 x^{12}$
  3. $8 x^{12}$
  4. $2 x^{16}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
${\left( 16{x}^{16} \right)}^{\cfrac{3}{4}} = {\left( {2}^{4} {x}^{16} \right)}^{\cfrac{3}{4}}$
$\Rightarrow \; = {\left( {2}^{4} \right)}^{\cfrac{3}{4}} {\left( {x}^{16} \right)}^{\cfrac{3}{4}}$

$\Rightarrow \; = {2}^\left( {4 \times \cfrac{3}{4}} \right)  {x}^\left({16 \times \cfrac{3}{4}} \right)$

$\Rightarrow \; = {2}^{3} \times {x}^{12}$

$\Rightarrow \; = 8{x}^{12}$
Multiple choice maths power and exponent power of powers laws of exponents and powers law of indices

Simplify the following $(3r^2)\times (9r^2)^{3/2} \div (27r^{-3})^{1/3}$ and find the power of $r$.

  1. $5$
  2. $2$
  3. $7$
  4. $6$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We have,
$(3r^2)\times (9r^2)^{3/2}\div(27r^{-3})^{1/3}\$

$\Rightarrow (3r^2)\times ((3r)^2)^{3/2}\div(3^3r^{-3})^{1/3}\$
$\Rightarrow (3r^2)\times (3r)^{3}\div(3r^{-1})\$

$\Rightarrow (3r^2)\times (3^3r^3)\times(3^{-1}r)\\$
$\Rightarrow 27r^6$

So, the power of $r$ is $6$.

Hence, this is the answer.