Tag: square root

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Questions Related to square root

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

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

  1. $91$
  2. $81$
  3. $21$
  4. $54$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

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

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

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

$=91$

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

Evaluate and state true or false 

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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 }  } $
$=\sqrt { \frac { 3^ 4\times 7^ 2\times 13^ 2 }{ 5^ 2\times 11^ 2\times 2^ 2 }  }$
$=\frac { 3^ 2\times 7\times 13 }{ 5\times 11\times 2 }$
$=\frac{819}{110}$
$=7\frac{49}{110}$

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

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

  1. $6\, \displaystyle \frac{19}{37}$
  2. $4\, \displaystyle \frac{2}{11}$
  3. $7\, \displaystyle \frac{2}{121}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

  1. $\displaystyle \frac { 16}{ 81 }$
  2. $\displaystyle \frac { 25}{ 81 }$
  3. $\displaystyle \frac { 4}{ 9}$
  4. $\displaystyle \frac { 2}{ 3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 } $

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

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

  1. $81$
  2. $131$
  3. $11$
  4. $123$
Reveal answer Fill a bubble to check yourself
B Correct answer
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, $25$ $+$ $y^{2}$ $\rightarrow$ $156$
 $y^{2}$ $\rightarrow$ $156-25$ $\rightarrow$ $131$
Multiple choice maths square root square root of perfect square finding square root of a number square root of a perfect square

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

  1. 7777

  2. 77.77

  3. 777.7

  4. 7.777
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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