Tag: square root

Questions Related to square root

The square root of $\displaystyle \frac{441}{961}$ is :

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

  1. $\displaystyle \frac{21}{39}$

  2. $\displaystyle \frac{37}{21}$

  3. $\displaystyle \frac{21}{31}$

  4. $\displaystyle \frac{11}{13}$

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Correct Option: C
Explanation:

We have to find square root of $\displaystyle \frac {441}{961}$

$\therefore \displaystyle \frac{\sqrt{144}}{\sqrt{961}}=\frac{21}{31}$

What smallest number must be added to 269 to make it a perfect square:

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

  1. 31

  2. 16

  3. 7

  4. 20

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Correct Option: D
Explanation:
$269$ lies between $256$ and $289$, which are squares of $16$ and $17$, respectively.
Hence, $17^{2} - 269 = 20$.
$\therefore$ We need to add $20$ to $269$ to make it a perfect square.

$\sqrt {\displaystyle \frac{0.289}{0.00121}}\, =\, ?$

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

  1. $\displaystyle \frac{1.7}{11}$

  2. $\displaystyle \frac{17}{11}$

  3. $\displaystyle \frac{170}{11}$

  4. $\displaystyle \frac{17}{110}$

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Correct Option: C
Explanation:

$\displaystyle {\sqrt {\frac{0.289}{0.00121}}\, =\, \sqrt {\frac{0.28900}{0.00121}}\, =\, \sqrt {\frac{28900}{121}}}$ $=\cfrac{170}{11}$

$\displaystyle \frac{?}{\sqrt{2.25}}\, =\, 550$

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

  1. 825

  2. 82.5

  3. 3666.66

  4. 2

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Correct Option: A
Explanation:
Let $ \cfrac{x}{\sqrt{2.25}} = 550$
Then, $ \cfrac{x}{1.5} = 550$
$\therefore x = (550 \times 1.5) =  {\left (\cfrac{550 \times 15}{10} \right ) = 825}$

$\sqrt{4\displaystyle\frac{57}{196}}=?$

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

  1. $2\displaystyle\frac{1}{14}$

  2. $2\displaystyle\frac{3}{14}$

  3. $2\displaystyle\frac{5}{14}$

  4. $2\displaystyle\frac{9}{14}$

Show answer
Correct Option: A
Explanation:

$\sqrt{4\frac{57}{196}}$
$=\sqrt{\frac{841}{196}}$
$=\frac{29}{14}$
$=2\frac{1}{14}$

The value of $\sqrt{0.064}$ is

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

  1. 0.8

  2. 0.08

  3. 0.008

  4. 0.252

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Correct Option: D
Explanation:
$\sqrt{0.064} = \sqrt{0.0640}$

$=  {\sqrt{\cfrac{640}{10000}} = \cfrac{\sqrt{640}}{100}}$

$=  \cfrac{25.2}{100} = 0.252$

$\sqrt{0.0009}\, \div\, \sqrt{0.01}\, =\, ?$

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

  1. 3

  2. 0.3

  3. $\displaystyle \frac{1}{3}$

  4. None of these

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Correct Option: B
Explanation:
$\sqrt{0.0009} \div \sqrt{0.01}$ $=  \cfrac{\sqrt{0.0009}}{\sqrt{0.01}}$
$= \cfrac{\sqrt{0.0009}}{\sqrt{0.0100}} $
$= \sqrt{\cfrac{9}{100}}$
$= \cfrac{\sqrt{9}}{\sqrt{100}}$
$ = \cfrac{3}{10} = 0.3$

The value of $\sqrt{214+\sqrt{130-\sqrt{88-\sqrt{44+\sqrt{25}}}}}$

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

  1. $14$

  2. $15$

  3. $16$

  4. $17$

Show answer
Correct Option: B
Explanation:

 $\sqrt{214+\sqrt{130-\sqrt{88-\sqrt{44+\sqrt{25}}}}}$
$\Rightarrow \sqrt{214+\sqrt{130-\sqrt{88-\sqrt{44+5}}}}$
$\Rightarrow \sqrt{214+\sqrt{130-\sqrt{88-\sqrt{49}}}}$
$\Rightarrow \sqrt{214+\sqrt{130-\sqrt{88-7}}}$
$\Rightarrow \sqrt{214+\sqrt{130-\sqrt{81}}}$
$\Rightarrow  \sqrt{214+\sqrt{130-9}}$
$\Rightarrow \sqrt{214+\sqrt{121}}$
$\Rightarrow \sqrt{214+11}$
$\Rightarrow \sqrt{225}=15$

The value of $\displaystyle \sqrt{1 + 2008 \sqrt{1 + 2009 \sqrt{1 + 2010 \sqrt{1 + 2011.2013}}}}$ is .............

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

  1. 2009

  2. 2010

  3. 2011

  4. 2013

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Correct Option: A
Explanation:

$\sqrt{1+2008\sqrt{1+2009\sqrt{1+2010\sqrt{1+2011.2013}}}}$
Or $\sqrt{1+2008\sqrt{1+2009\sqrt{1+2010.2012}}}$
$\Rightarrow \sqrt{1+2008\sqrt{1+2009.2011}}$
$\Rightarrow \sqrt{1+2008.2010}$
$\Rightarrow \sqrt{4036081}=2009$

Find the square root of the following $\displaystyle\frac{2025}{4900}$

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

  1. $\displaystyle\frac{55}{80}$

  2. $\displaystyle\frac{55}{70}$

  3. $\displaystyle\frac{45}{80}$

  4. $\displaystyle\frac{45}{70}$

Show answer
Correct Option: D
Explanation:

Let us find the square root of $2025\;and\;4900$ by factorising them.
$3\mid \; \; 2025\ { \overline { 3\mid \; \; 675 }  }\ { \overline { 3\mid \; \; 225 }  }\ { \overline { 3\mid \; \; \; \; 75 }  }\ { \overline { 5\mid \; \; \; \; 25 }  }\ { \overline { 5\mid \; \; \; \; \; 5 }  }\ { \overline { \; \; \mid \; \; \; \; 1 }  }$
$2025=\underline{3\times3}\times\underline{3\times3}\times\underline{5\times5}$
$\sqrt{2025}=3\times3\times5=45$
$2\mid \; \; 4900\ { \overline { 2\mid \; \; 2450 }  }\ { \overline { 5\mid \; \; 1225 }  }\ { \overline { 5\mid \; \; \; \; 245 }  }\ { \overline { 7\mid \; \; \; \; \;49 }  }\ { \overline { 7\mid \; \; \; \; \; \;7 }  }\ { \overline { \; \; \;\mid \; \; \; \; \;1 }  }$
$4900=\underline{2\times2}\times\underline{5\times5}\times\underline{7\times7}$
$\sqrt{4900}=2\times5\times7=70$
So, $\cfrac{\sqrt{2025}}{\sqrt{4900}}=\cfrac{45}{70}$.