Tag: maths

Questions Related to maths

The square root of $289$ is?

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

  1. $13$

  2. $17$

  3. $27$

  4. $23$

Show answer
Correct Option: B
Explanation:

$289 = 17 × 17$
$\text{So, square root of 289 is 17.}$ 

Simplify the following: 
$\displaystyle \frac{\sqrt{24}}{8}+\frac{\sqrt{54}}{9}$ is equal to $\displaystyle \frac{7\sqrt{6}}{12}$
If true then enter $1$ and if false then enter $0$

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

  1. $1$

  2. $0$

  3. Cannot be determined, incomplete information

  4. None of the above

Show answer
Correct Option: A
Explanation:

$ =\dfrac { 9\sqrt { 2\times 2\times 2\times 3 } +8\sqrt { 2\times 3\times 3\times 3 }  }{ 72 } $
$ = \dfrac { 18\sqrt { 6 } +24\sqrt { 6 }  }{ 72 } $
$ = \dfrac { 42\sqrt { 6 }  }{ 72 } $
$ = \dfrac { 7\sqrt { 6 }  }{ 12 }  $

The value of $\cfrac { 10\sqrt { 6.25 }  }{ \sqrt { 6.25} - 0.5 } $ is
maths square root square root of perfect square finding square root of a number square root of a perfect square

  1. $125$

  2. $0.125$

  3. $1.25$

  4. $12.5$

Show answer
Correct Option: D
Explanation:

$\cfrac { 10\sqrt { 6.25 }  }{ \sqrt { 6.25-0.5 }  } =\cfrac { 10\times 2.5 }{ 2.5-0.5 } =\cfrac { 25 }{ 2 } =12.5$

If ${\left( {\dfrac{m}{n}} \right)^{\dfrac{3}{8}}} + {\left( {\dfrac{n}{m}} \right)^{\dfrac{3}{8}}} = 9$ then find the value of ${\left( {\dfrac{m}{n}} \right)^{\dfrac{3}{4}}} + {\left( {\dfrac{n}{m}} \right)^{\dfrac{3}{4}}}$

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

  1. $79$

  2. $72$

  3. $83$

  4. $84$

Show answer
Correct Option: A
Explanation:
$(\dfrac{m}{n})^\dfrac{3}{8}+(\dfrac{n}{m})^\dfrac{3}{8}=9$
$[(\dfrac{m}{n})^\dfrac{3}{8}+(\dfrac{n}{m})^\dfrac{3}{8}]^{2} =9^{2}$
$ ((\dfrac{m}{n})^\dfrac{3}{8})^{2}+((\dfrac{n}{m})^\dfrac{3}{8})^{2}+2((\dfrac{m}{n})^\dfrac{3}{8})((\dfrac{n}{m})^\dfrac{3}{8})=81$
$ (\dfrac{m}{n})^\dfrac{3}{4}+(\dfrac{n}{m})^\dfrac{3}{4}=81-2=79$

The square root of sum of the digits in the square of $121$ is

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

  1. $4$

  2. $3$

  3. $6$

  4. $9$

Show answer
Correct Option: A
Explanation:
${ \left( 121 \right)  }^{ 2 }$

$={ \left( 100+21 \right)  }^{ 2 }$     

$={ 100 }^{ 2 }+{ 21 }^{ 2 }+2\left( 100 \right) \left( 21 \right) $      $[\because (a+b)^2= a^2+2ab+b^2]$

$=14641$

Sum of digits $=1+4+6+4+1=16$

Square root$=\sqrt { 16 } =4$

Find the square root of $225$ using "Repeated Subtraction".

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

  1. $11$

  2. $15$

  3. $5$

  4. $8$

Show answer
Correct Option: B
Explanation:

$\\225-1=224\\224-3=221\\221-5=216\\216-7=209\\209-9=200\\200-11=189\\189-13=176\\176-15=161\\161-17=144\\144-19=125\\125-21=104\\104-23=81\\81-25=56\\56-27=29\\29-29=0\\\>Total\>steps\>of\>=15\>\\hence\>\sqrt{225}=15$

Evaluate and state true or false 

$\displaystyle \sqrt{\frac{25}{32}\, \times\, 2\frac{13}{18}\, \times\, 0.25}$ is $\displaystyle \frac{35}{48}$

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

   $\sqrt{\dfrac{25}{32} \times 2\dfrac{13}{18}\times 0.25}$
$=\sqrt { \dfrac { 25 }{ 32 } \times \dfrac { 49 }{ 18 } \times \dfrac { 25 }{ 100 }  } $
$=\sqrt { \dfrac { 5^ 2 }{ 2^ 5 } \times \dfrac { 7^ 2 }{ 9\times 2 } \times \dfrac { 1 }{ 2^ 2 }  } $
$=\sqrt { \dfrac { 5^ 2 }{ 2^ 6 } \times \dfrac { 7^ 2 }{ 3^2 } \times \dfrac { 1 }{ 2^ 2 }  } $
$=\dfrac{5\times 7}{2^4\times 3}$
$=\dfrac{35}{48}$

For each of the following, find the least number that must be added so that the resulting number is a perfect square. 7172

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

  1. 23

  2. 65

  3. 15

  4. 53

Show answer
Correct Option: D

The square root of $\displaystyle96\frac{1}{25}$ is $\displaystyle9\frac{4}{5}$
State true or false.

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Given number is $ 96\frac {1}{25} = \frac {2401}{25} $

Square root of $ \frac {2401}{25} =  \frac { \sqrt {2401}}{\sqrt {25}}

= \frac {49}{5} = 9 \frac {4}{5} $

Find the least number that must be subtracted so that the resulting number is a perfect square.
1886

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

  1. 27

  2. 47

  3. 37

  4. 85

Show answer
Correct Option: C