Question

Find the least no. Which must be added to 8400 to obtain a perfect square. Find it and it square root

Answer 1

91^2 = 8281 is less then 8400
92^2 = 8464 is greater then 8400

so, 92^2-91^2
=8464 - 8400

= 64 is the least number.

Answer 2

The number which needs to be added is 64 and its square root is 92

Step-by-step explanation:

We know that,

$90 \times 90=8100$

$91 \times 91=8281$

$92 \times 92=8464$

8400 is in between the squares of the numbers 91 and 92

Consider,

$(92 \times 92)-(91 \times 91)=8464-8281=64$

Therefore, the least number is 64 which must be added to 8400 to get the perfect square.

$64+8400=8464$

$\Rightarrow \sqrt{8464}=92$

Thus, the square root of the number 8464 is 92.