Tag: square root

Questions Related to square root

Square root of $400$ is?

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

  1. $40$

  2. $25$

  3. $20$

  4. $100$

Show answer
Correct Option: C
Explanation:

$400=2\times 200$

       $=2\times 2\times 100$
       $=2\times 2\times 2\times 50$
       $=2\times 2\times 2\times 2\times 25$
       $=2\times 2\times 2\times 2\times 5\times 5$
       $=2^4\times 5^2$
$\Rightarrow$  $400=2^4\times 5^2$
$\Rightarrow$  $\sqrt{400}=\sqrt{2^4\times 5^2}$
$\Rightarrow$  $\sqrt{400}=2^2\times 5$
$\Rightarrow$  $\sqrt{400}=4\times 5$
$\Rightarrow$  $\sqrt{400}=20$

The value  of  $\sqrt {11 - \sqrt{112} }=  $

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

  1. $2 + \sqrt{7}$

  2. $2 - \sqrt{7}$

  3. $ \sqrt{7} - 2$

  4. none of these

Show answer
Correct Option: C
Explanation:
$11-\sqrt {112}$

$=11-\sqrt {4\times 28}$

$=11-\sqrt {4}\times \sqrt {28}$

$=11-2\times \sqrt {28}$

$=11-2\times \sqrt {7}\times \sqrt {4}$

$=7+4-2\times \sqrt {7}\times \sqrt {4}$

$=(\sqrt {7})^2 +(\sqrt {4})^2 -2\times \sqrt {7}\times \sqrt {4}$

$=(\sqrt {7}-\sqrt {4})^2$

Thus, $11-\surd {112}=(\surd {7} -\surd {4})^2$

Hence,

$\sqrt {11-\sqrt {112}}=\sqrt {(\sqrt {7}-\sqrt {4})^2}=\sqrt {7}-\sqrt {4}=\sqrt {7}-2$

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

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Correct Option: D