Question

Find the least number that must be added to 1300 so as to get a perfect square. Also find the square root of the perfect square? [3 MARKS]

Answer 1

Concept : 1 Mark
Division method : 1 Marks
Conclusion : 1 Mark

Applying the long division method we have,

$\begin{array}{cc}& 36\\ 3& 1300\\ & 9\\ 6& 400\\ & 396\\ & 4\end{array}$

From above, it is clear that given number 1300 is greater than $(36{)}^2$

i.e., ${36}^2<1300<{37}^2$

i.e., $1296<1300<1369$

1369 - 1300 = 69

The required number is 69.

The square root of 1369 is 37.