Tag: square root

Questions Related to square root

For what value of $\displaystyle x+\frac { 1 }{ 4 } \sqrt { x } +{ a }^{ 2 }$ will be perfect square -

  1. $\displaystyle \pm { 1 }/{ 18 }$

  2. $\displaystyle \pm { 1 }/{ 8 }$

  3. $\displaystyle \pm { 1 }/{ 5 }$

  4. $\displaystyle { 1 }/4$


Correct Option: B
Explanation:

If $\displaystyle x+\frac { 1 }{ 4 } \sqrt { x } +{ a }^{ 2 }$ is a perfect square
then $\displaystyle \frac { 1 }{ 4 } \sqrt { x } =2\times \sqrt { x } \times \left( \pm a \right) $
$\displaystyle \therefore \quad a=\pm \frac { 1 }{ 8 } $

Solve:
$ \sqrt { 225 } -x=0 ,x=?$
  1. $10$

  2. $4$

  3. $15$

  4. $5$


Correct Option: C
Explanation:
$\sqrt { 225 } =15$
$\sqrt { 225 } -x=0$
$15-x=0$
$x=15$