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

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

  1. $\displaystyle \frac{21}{39}$
  2. $\displaystyle \frac{37}{21}$
  3. $\displaystyle \frac{21}{31}$
  4. $\displaystyle \frac{11}{13}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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

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

  1. $\displaystyle \frac{1.7}{11}$
  2. $\displaystyle \frac{17}{11}$
  3. $\displaystyle \frac{170}{11}$
  4. $\displaystyle \frac{17}{110}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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

  1. $14$
  2. $15$
  3. $16$
  4. $17$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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

  1. 2009

  2. 2010

  3. 2011

  4. 2013
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

  1. $\displaystyle\frac{55}{80}$
  2. $\displaystyle\frac{55}{70}$
  3. $\displaystyle\frac{45}{80}$
  4. $\displaystyle\frac{45}{70}$
Reveal answer Fill a bubble to check yourself
D Correct answer
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, $\cfrac{\sqrt{2025}}{\sqrt{4900}}=\cfrac{45}{70}$.