Tag: square root

Questions Related to square root

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

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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

Evaluate: $\displaystyle\sqrt{\left (5\, +\, 2\frac{21}{25}\right )\, \times\, \frac{0.169}{1.6}}$ $\times 100$

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

  1. $91$

  2. $81$

  3. $21$

  4. $54$

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Correct Option: A
Explanation:

$\sqrt{\left (5+2\dfrac{21}{25}\right )\times \dfrac{0.169}{1.6}}\times 100$

$=\sqrt{\left (5+\dfrac{71}{25}\right )\times \dfrac{169\times 10}{16\times 1000}}\times 100$

$=\sqrt{\left (\dfrac{125+71}{25}\right )\times \dfrac{169}{16\times 100}}\times 100$

$=\sqrt{\left (\dfrac{196}{25}\right )\times \dfrac{169}{16\times 100}}\times 100$

$=\dfrac{14}{5}\times \dfrac{13}{4\times 10}\times 100$

$=\dfrac{91}{100}\times 100$

$=91$

Evaluate and state true or false 

$\displaystyle \sqrt{1\frac{4}{5}\,\times\, 14\frac{21}{44}\, \times\, 2\frac{7}{55}}$ is $\displaystyle7\frac{49}{110}$

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:

   $\sqrt { 1\frac { 4 }{ 5 } \times 14\frac { 21 }{ 44 } \times 2\frac { 7 }{ 55 }  }$
$=\sqrt { \frac { 9 }{ 5 } \times \frac { 637 }{ 44 } \times \frac { 117 }{ 55 }  } $
$=\sqrt { \frac { 3^ 2 }{ 5 } \times \frac { 7^ 2\times 13 }{ 11\times 4 } \times \frac { 13\times 9 }{ 11\times 5 }  } $
$=\sqrt { \frac { 3^ 4\times 7^ 2\times 13^ 2 }{ 5^ 2\times 11^ 2\times 2^ 2 }  }$
$=\frac { 3^ 2\times 7\times 13 }{ 5\times 11\times 2 }$
$=\frac{819}{110}$
$=7\frac{49}{110}$

Evaluate: $\sqrt{100}+\sqrt{49}$.

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

  1. $\sqrt{149}$

  2. $\sqrt{490}$

  3. $\sqrt{10}+\sqrt{14}$

  4. $17$

Show answer
Correct Option: D
Explanation:

$\sqrt{100}+\sqrt{49}= 10 + 7 = 17.$

Thus the correct option is D.

The square root of $42\, \displaystyle \frac{583}{1369}$ is :

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

  1. $6\, \displaystyle \frac{19}{37}$

  2. $4\, \displaystyle \frac{2}{11}$

  3. $7\, \displaystyle \frac{2}{121}$

  4. None of these

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Correct Option: A
Explanation:

$\sqrt{42\, \displaystyle \cfrac{583}{1369}}\, =\, \sqrt{\displaystyle \cfrac{58081}{1369}}$
$=\, \displaystyle \cfrac{\sqrt{58081}}{\sqrt{1369}}$
$=\, \displaystyle \cfrac{241}{37}\, =\, 6\, \displaystyle \cfrac{19}{37}$

Evaluate $\sqrt{41-\sqrt{21+\sqrt{19-\sqrt{9}}}}$

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

  1. $3$

  2. $5$

  3. $6$

  4. $6.4$

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Correct Option: C
Explanation:

$\sqrt{41-\sqrt{21+\sqrt{19-\sqrt{9}}}}\=\sqrt{41-\sqrt{21+\sqrt{19-3}}}\=\sqrt{41-\sqrt{21+\sqrt{16}}}\=\sqrt{41-\sqrt{21+4}}\=\sqrt{41-\sqrt{25}}\=\sqrt{41-5}=\sqrt{36}=6$

Evaluate  $\sqrt {\displaystyle \frac { 25 }{ 81 } -\displaystyle\frac { 1 }{ 9 }  } $

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

  1. $\displaystyle \frac { 16}{ 81 }$

  2. $\displaystyle \frac { 25}{ 81 }$

  3. $\displaystyle \frac { 4}{ 9}$

  4. $\displaystyle \frac { 2}{ 3}$

Show answer
Correct Option: C
Explanation:

$\sqrt {\displaystyle \frac { 25 }{ 81 } -\displaystyle\frac { 1 }{ 9 }  } =\sqrt { \displaystyle\frac { 25-9 }{ 81 }  } =\sqrt {\displaystyle \frac { 16 }{ 81 }  } =\displaystyle\frac { \sqrt { 16 }  }{ \sqrt { 81 }  } =\displaystyle\frac { 4 }{ 9 } $

The sum of the squares of $2$ numbers is $156$. If the one number is $5$, the square of the other number is

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

  1. $81$

  2. $131$

  3. $11$

  4. $123$

Show answer
Correct Option: B
Explanation:
Let the two numbers be $x$ and $y$.
$x^{2}$ $+$ $y^{2}$ $\rightarrow$ $156$
${x}$ $\rightarrow$ 5
$x$ $\rightarrow$ $5\times5$ $\rightarrow$ $25$
Substituting, $25$ $+$ $y^{2}$ $\rightarrow$ $156$
 $y^{2}$ $\rightarrow$ $156-25$ $\rightarrow$ $131$

If $\sqrt{49}=7$, then find the value of $\sqrt{49}+\sqrt{0.49}+\sqrt{0.0049}+\sqrt{0.000049}$

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

  1. 7777

  2. 77.77

  3. 777.7

  4. 7.777

Show answer
Correct Option: D
Explanation:

$\sqrt{49}+\sqrt{0.49}+\sqrt{0.0049}+\sqrt{0.000049}\=7+\sqrt { \displaystyle\frac { 49 }{ 100 }  } +\sqrt {\displaystyle \frac { 49 }{ 10000 }  } +\sqrt { \displaystyle\frac { 49 }{ 1000000 }  } \ =7+\displaystyle\frac { \sqrt { 49 }  }{ \sqrt { 100 }  } +\displaystyle\frac { \sqrt { 49 }  }{ \sqrt { 10000 }  } +\displaystyle\frac { \sqrt { 49 }  }{ \sqrt { 1000000 }  } \ =7+\displaystyle\frac { 7 }{ 10 } +\displaystyle\frac { 7 }{ 100 } +\displaystyle\frac { 7 }{ 1000 } \ =7+0.7+0.07+0.007\ =7.777$