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 maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Simplify : 

$\displaystyle \sqrt{2}\times \sqrt[3]{3} \times \sqrt[4]{4}$.

  1. $\sqrt[3]{12}$
  2. $\sqrt[3]{24}$
  3. $\sqrt[3]{20}$
  4. $\sqrt[3]{25}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$ \sqrt{2} \times \sqrt[3] {3} \times \sqrt[4]{4}$
$=2^{ \frac { 1 }{ 2 }  } \times 3^{ \frac { 1 }{ 3 }  }\times 2^{ \frac { 2 }{ 4 }  }$
$=2^{ \frac { 1 }{ 2 }  } \times 2^{ \frac { 1 }{ 2 }  }\times 3^{ \frac { 1 }{ 3 }  }$
$=2  \times3^{ \frac { 1 }{ 3 }  }$
$=2^{ \frac { 3 }{ 3 }  }\times3^{ \frac { 1 }{ 3 }  }  $
$=\sqrt [ 3 ]{ 2^{ 3 } }\times\sqrt[3]{3}$
$=\sqrt[3]{8\times3}$
$=\sqrt[3]{24}$

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Simplify by combining similar terms :$\displaystyle 3\sqrt{147}-\frac{7}{3}\sqrt{\frac{1}{3}}+7\sqrt{\frac{1}{3}}$

  1. $\displaystyle \frac{189}{3\sqrt{3}}$
  2. $\displaystyle \frac{175}{3\sqrt{3}}$
  3. $\displaystyle \frac{208\sqrt{3}}{3}$
  4. $\displaystyle \frac{203}{3\sqrt{3}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simplify the expression: 3*sqrt(147) = 3*sqrt(49*3) = 21*sqrt(3). The other terms are -(7/3)(1/sqrt(3)) + 7(1/sqrt(3)) = (14/3)*(1/sqrt(3)) = 14/(3*sqrt(3)). Combining these requires a common denominator. The result is (21*3*sqrt(3) + 14)/(3*sqrt(3)) = (189+14)/(3*sqrt(3)) = 203/(3*sqrt(3)).

Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

Simplify $(9^{4/3} \div 27^{2/3}) \times 3^{3/2}$

  1. $3^{9/5}$
  2. $3^{13/6}$
  3. $3^{37/6}$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle \left ( \left ( 3^2 \right )^{4/3} \div \left ( 3^3 \right )^{2/3} \right ) \times 3^{3/2}$
$= 3^{8/3} \div 3^2 \times 3^{3/2}$
$= \displaystyle 3^{8/3 - 2 + 3/2} $
$= \displaystyle  3^{ \displaystyle \frac{16 - 12 + 9}{6}}$
$= 3^{13/ 6}$

Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

Simplify : $\displaystyle\frac{9^{5/2}-3\times7^0-\begin{pmatrix}\displaystyle\frac{1}{81}\end{pmatrix}^{-\displaystyle\frac{1}{2}}}{(27)^{2/3}-\begin{pmatrix}\displaystyle\frac{8}{27}\end{pmatrix}^{2/3}}$

  1. $0$
  2. $16$
  3. $27$
  4. $77$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$
\frac { { 9 }^{ \frac { 5 }{ 2 }  }-{ 3\times 7 }^{ 0 }{ \quad -\frac { 1 }{ 81 }  }^{ -\frac { 1 }{ 2 }  } }{ { 27 }^{ \frac { 2 }{ 3 }  }-(\frac { 8 }{ 27 } )^{ \frac { 2 }{ 3 }  } } \quad \quad \ \ NR\quad =\quad { 3 }^{ 2\times \frac { 5 }{ 2 }  }-3-(\frac { 1 }{ 81 } )^{ -\frac { 1 }{ 2 }  }\quad =\quad { 3 }^{ 5 }-3-({ 3 }^{ -4\times \frac { -1 }{ 2 }  })\quad =243-3-9=\quad 231\quad \ Dr\quad =\quad { 3 }^{ 3\times \frac { 2 }{ 3 }  }-(\frac { 2 }{ 3 } )^{ 3\times \frac { 2 }{ 3 }  }\quad =\quad 9\quad -\quad \frac { 4 }{ 9 } \quad =\quad 77/9\ \frac { Dr }{ Nr } \quad =\quad \frac { 231 }{ 77/9 } \quad =\quad 3\times 9\quad =\quad 27
$

Multiple choice

Simplify √48

  1. 4√2

  2. 4√3

  3. 5√3

  4. 2√5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

sqrt(48) = sqrt(16 * 3) = 4*sqrt(3).

Multiple choice

Simplify √90

  1. 3√10

  2. 9√10

  3. 3√20

  4. 3√15
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

sqrt(90) = sqrt(9 * 10) = 3*sqrt(10).

Multiple choice

Simplify √88

  1. 5√11

  2. 4√11

  3. 2√22

  4. 4√22
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

sqrt(88) = sqrt(4 * 22) = 2*sqrt(22).

Multiple choice

Simplify √50

  1. 5√3

  2. 4√2

  3. 10√2

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

sqrt(50) = sqrt(25 * 2) = 5*sqrt(2).

Multiple choice

Simplify √363

  1. 5√7

  2. 3√11

  3. 11√3

  4. 7√5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

sqrt(363) = sqrt(121 * 3) = 11*sqrt(3).

Multiple choice

Simplify √128

  1. 8√2

  2. 4√32

  3. 2√8

  4. 32√4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To simplify the square root, find the largest perfect square factor of 128. Since 128 = 64 * 2, the square root is sqrt(64) * sqrt(2), which equals 8 * sqrt(2).

Multiple choice

Simplify √600

  1. 10√6

  2. 2√150

  3. 150√2

  4. 6√10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To simplify sqrt(600), identify the largest perfect square factor, which is 100. Thus, sqrt(600) = sqrt(100 * 6) = 10 * sqrt(6).

Multiple choice

Simplify √147

  1. 9√3

  2. 3√7

  3. 3√5

  4. 7√3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The number 147 can be factored into 49 * 3. Since 49 is a perfect square, sqrt(147) = sqrt(49) * sqrt(3) = 7 * sqrt(3).

Multiple choice

Simplify √8100

  1. 9√100

  2. 10√81

  3. 3√900

  4. 90
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The square root of 8100 is the square root of (81 * 100). This simplifies to sqrt(81) * sqrt(100) = 9 * 10 = 90.