Question

The smallest number which when added to the sum of squares of 9 to 10 gives a perfect square

Answer 1

Step-by-step explanation:

9^2+10^2=181

nearest square is 14^2=196

hence, 196-181=15 must be added to make it perfect square.

Answer 2

15 must be added to the sum of squares of 9 to 10 gives a perfect square

Solution:

Given that,

We have to find the smallest number which when added to the sum of squares of 9 to 10 gives a perfect square

Let "x" be the smallest number that when added to the sum of squares of 9 to 10 gives a perfect square

So, we can say,

$9^2 + 10^2 + x = perfect\ square\ number\\\\81 + 100 + x =perfect\ square\ number\\\\181 + x = perfect\ square\ number$

Now the nearest perfect square of 181 is 196

$196 = 14 \times 14 = 14^2$

Therefore,

181 + x = 196

x = 196 - 181

x = 15

Thus, 15 must be added to the sum of squares of 9 to 10 gives a perfect square

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