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 maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

Multiply and reduce to lowest form:
$\cfrac { 2 }{ 3 } \times 5\cfrac { 1 }{ 5 } $

  1. $3\cfrac { 7 }{ 15 } $
  2. $7\cfrac { 3 }{ 15 } $
  3. $\cfrac { 7 }{ 15 } $
  4. $3\cfrac { 3 }{ 15 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\dfrac{2}{3}\times 5\dfrac{1}{5}$


Can be written as


$\dfrac{2}{3}\times \dfrac{26}{5}$

$=\dfrac{52}{15}$

$=3\dfrac{7}{15}$

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

$4\frac{4}{5}\div\frac{3}{5}$ of $5+\frac{4}{5}\times\frac{3}{10} -\frac{1}{5}$ is simplified, then the result is

  1. $1\frac{16}{25}$
  2. $1\frac{17}{25}$
  3. $\frac{40}{25}$
  4. $\frac{42}{25}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Apply BODMAS
$4\frac{4}{5}\div\frac{3}{5}$ of $5+\frac{4}{5}\times\frac{3}{10} -\frac{1}{5}$
$=\frac{24}{5}\div3+\frac{4}{5\times\frac{3}{10}-\frac{1}{5}}$
$=\frac{8}{5}+\frac{6}{25}-\frac{1}{5}$
$=\frac{41}{25}$
$=1\frac{16}{25}$
Option 'A' is the answer

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).