Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

The simplest rationalizing factor of $\sqrt{75}$ is.

  1. $(75)^{1/3}$
  2. $5\sqrt3$
  3. $3$
  4. $\sqrt{150}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let us first factorize $75$ as shown below:


$75=3\times 5\times 5=3\times { 5 }^{ 2 }$

Now consider $\sqrt {75}$ as follows:

$\sqrt { 75 } =\sqrt { 3\times 5\times 5 } =\sqrt { 3\times { 5 }^{ 2 } } =\sqrt { 3 } \times \sqrt { { 5 }^{ 2 } } =5\sqrt { 3 }$

Hence, the simplest rationalizing factor of $\sqrt {75}$ is $5\sqrt { 3 }$.

Multiple choice maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

The value of $\displaystyle\ \frac{15\times (-24)\times-18}{-(27)\times (20)}$ is

  1. -16

  2. -15

  3. -12

  4. 12
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

As there are $ 2 $ negative numbers in the numerator and $ 1 $ in the denominator, the answer will be negative. 

Cancelling out the common factors and simplifying we get 


$ \dfrac { 15\times (-24)\times -18 }{ -(27)\times (20) } =\dfrac {3 \times 8 \times 18}{-9\times 4}=-3\times 2\times2 = -12 $


Multiple choice maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

Divide:
$(-60 \times -72)  \  by\    (36\times (-15))$

  1. -8

  2. -16

  3. 8

  4. 16
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, $

\dfrac { (-60)\times (-72) }{ 36\times (-15) } $

As there are $ 2 $ negative numbers in the numerator and $ 1 $ in the

denominator, the answer will be negative.

Cancelling out the common factors and simplifying we get

$ \dfrac { (-60)\times (-72) }{ 36\times (-15) }=-4\times 2  = - 8 $

Multiple choice maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

Evaluate $\displaystyle\ \frac{(-8)\times8\times(-8)\times(-8)}{(-4)\times(-4)\times(-4)\times(-4)}$

  1. -1

  2. -6

  3. -16

  4. 16
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $

\dfrac { (-8) \times 8 \times (-8) \times (-8) }{ (-4)\times (-4) \times (-4) \times (-4) } $

As there are $ 3 $ negative numbers in the numerator and $ 4 $ in the denominator, the answer will be negative.

Canceling out the common factors and simplifying we get

$ \dfrac { (-8) \times 8 \times (-8) \times (-8) }{ (-4)\times (-4) \times (-4) \times (-4) }   =2\times -2\times2\times2 = - 16 $