Question

Find the least 2-digit whole number N so that the sum 2^9+2^4+N is a perfect square.

Answer 1

Answer:

N=48

Step-by-step explanation:

2^9+2^4+48=576

576 is a perfect square

Answer 2

The least value of N that makes $2^9 + 2^4 + N$ a perfect square is 48

The number is given as:

$2^9 + 2^4 + N$

Evaluate the exponents

$2^9 + 2^4 + N = 512 + 16 + N$

Add 512 and 16

$2^9 + 2^4 + N = 528 + N$

The above equation means that:

• The sum of 528 and N is greater than 537 (this is so because N is 2-digit i.e. the possible value of N starts from 10).
• The smallest perfect square greater than 537 is 576.

So, the smallest value of the equation is 576.

The equation becomes

$528 + N = 576$

Subtract 528 from both sides

$N = 576 - 528$

$N = 48$

Hence, the least value of N is 48

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