Question

Find the perfect square root number that is nearest to $252$.

Answer 1

Step 1: Compute the two nearest perfect square

Let us write the square of certain numbers that are nearer to $252$.

${14}^2=196$

${15}^2=225$

${16}^2=256$

${17}^2=289$

From the above,

${\left(15\right)}^2<252<{\left(16\right)}^2$

$\Rightarrow 225<252<256$

Step 2: Calculate the required perfect square

Upon calculating the difference between the two perfect squares,

$252–225=27$

$256–252=4$

Hence we can see that $256$ is nearer to $252$ than $225$.

Hence, the required perfect square root number is $256$.