Mathematics · Quantitative Aptitude

Surds and Indices

408 Questions

Surds and indices questions focus on evaluating square roots, cube roots, and fractional exponents. These topics are a core part of the quantitative aptitude section in many competitive exams. Practicing these problems builds speed and accuracy for solving numerical equations.

Square roots evaluationCube roots calculationExponents and powersFractional exponentsSurds multiplication

Surds and Indices Questions

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

Subtracting which odd number will get the value of 144 for the square root of the number 169 using repeated subtraction method?

  1. 3

  2. 5

  3. 7

  4. 9
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Repeated subtraction method: Subtract successive odd numbers from the given number starting from 1 till the difference becomes zero.
So, 169 - 1 = 168
168 - 3 = 165
165 - 5 = 160
160 - 7 = 153
153 - 9 = 144
9 is the odd number, subtracting with 153 to get the value of 144.

Multiple choice physics measurement and measuring instrument measuring distance of celestial bodies unconventional units of measurements units of mass

What is the value of $1  \ m $ in $\mathring{A}$?

  1. $10^{-10}$
  2. $10^{5}$
  3. $10^{7}$
  4. $10^{10}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$1 m = 10^{10} \mathring{A}$
or we can say 1 angstrom $=10^{-10} m$
The natural sciences and technology often uses angstrom to express sizes of atoms, molecules, microscopic biological structures, and lengths of chemical bonds, arrangement of atoms in crystals, wavelengths of electromagnetic radiation.

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

Which of the following expresses the power of quotient rule?

  1. $\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b^{m}}$
  2. $\left (\dfrac {a}{b}\right )^{m} = \left (\dfrac {a}{b}\right )^{m}$
  3. $\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b}$
  4. $\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b^{-m}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If the division of two bases is powered by the same exponent,

 then the result is division of both the bases, 
each powered by the given exponent.
$\therefore \left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b^{m}}$
So, option $A$ is correct.

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

Evaluate: $\displaystyle \left [ \left ( 4 \right )^{\tfrac{1}{4}}\times \left ( 2 \right )^{\tfrac{1}{2}}\times \left ( 5 \right )^{\tfrac{1}{5}} \right ]^{0}$

  1. $40$
  2. $0$
  3. $1$
  4. $10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

=$\displaystyle \left [ \left ( 4 \right )^{\tfrac{1}{4}}\times \left ( 2 \right )^{\tfrac{1}{2}} \times \left ( 5 \right )^{\tfrac{1}{2}}\right ]^{0}$

=$\displaystyle 4^{0}\times 2^{0}\times 5^{0}$
=$\displaystyle 1\times 1\times 1$
=$1$
So, option $C$ is correct.

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

Choose the correct option:
$\left[\dfrac{{100}}{{101}}\right]^3$

  1. $\dfrac{{100}^3}{{101}^3}$
  2. $\dfrac{{100}^4}{{101}^4}$
  3. $\dfrac{{1000}^2}{{101}^2}$
  4. $\dfrac{{100}}{{101}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Now\quad \left[ \dfrac { 100 }{ 101 }  \right] ^{ 3 }\quad \ \quad \quad =\quad \dfrac { { 10 }0^{ 3 } }{ 101^{ 3 } } \quad \left( \because \left( \dfrac { { a }^{ m } }{ { b }^{ m } }  \right) =\left( \dfrac { a }{ b }  \right) ^{ m } \right) \ $

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

Choose the correct options:$\dfrac{{10}^2}{{11}^2}$

  1. $\left[\dfrac{{10}}{{11}}\right]^2$
  2. $\left[\dfrac{{100}}{{11}}\right]^2$
  3. $\left[\dfrac{{10}}{{11}}\right]^4$
  4. $\left[\dfrac{{5}}{{11}}\right]^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Now\quad \dfrac { { 10 }^{ 2 } }{ 11^{ 2 } } \ =\quad \left( \dfrac { 10 }{ 11 }  \right) ^{ 2 }\left( \because \left( \dfrac { { a }^{ m } }{ { b }^{ m } }  \right) =\left( \dfrac { a }{ b }  \right) ^{ m } \right) $

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

Choose the correct option:
$\left(\dfrac{5^5\times6^5}{3^5}\right)$

  1. $\left(\dfrac{5\times6}{3}\right)^5$
  2. $\left(\dfrac{5\times6}{3}\right)^6$
  3. $\left(\dfrac{5\times6}{5}\right)^3$
  4. $\left(\dfrac{5\times6}{5}\right)^5$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Now\quad \left( \dfrac { { 5 }^{ 5 }\times { 6 }^{ 5 } }{ { 3 }^{ 5 } }  \right) \quad \ \quad \quad =\quad \left( \dfrac { 5\times 6 }{ 3 }  \right) ^{ 5 }\quad \left( \because \left( \dfrac { { a }^{ m }\times { c }^{ m } }{ { b }^{ m } }  \right) =\left( \dfrac { a\times c }{ b }  \right) ^{ m } \right) $