Question

how many two digit perfect squares​

Answer 1

Step-by-step explanation:

So, starting with highest two-digit number we have is 99 so sum of its digit is,

9+9=18

So, that means we will only consider the perfect square below 18 which are:

12=122=432=942=16

Now, we will write all the possible ways to find the sum of the above perfect square using two digits.

Firstly, 1 can be written as,

1=1+0

Next, 4 can be written as,

4=2+2=3+1=1+3

Next, 9 can be written as,

9=9+0=8+1=1+8=7+2=2+7=6+3=3+6=5+4=4+5

Next, 16 can be written as,

16=8+8=9+7=7+9

So, we can write the numbers for each perfect square as,

1:104:22,31,139:90,81,18,72,27,63,36,54,4516:88,97,79

Counting the above digit we get a total of 17.

So, there are 17 two-digit numbers whose sum of digits is a perfect square.

Note:

Perfect squares are those numbers which are formed when any number is multiplied by itself. In other words, we can say that if we find a square root of a perfect number we get an integer as the answer and not a decimal or fractional number. A number is a square only if it can be arranged that number point in a square. Sum of two consecutive triangular numbers forms a square. We should not get confused between the square and cube of a number. The number obtained is obtained by multiplying the number twice to itself.

Answer 2

Answer:

there are 17 two-digit numbers whose sum of digits is a perfect square. Note: Perfect squares are those numbers which are formed when any number is multiplied by itself.

Step-by-step explanation:

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