Question

Find the least number which must be added to 18,265 to obtain a perfect square.

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Answer 1

Step-by-step explanation:

In This Problem,

First,We have to find the square root of

18,265

It can be written as

√18265

The value of

√18265 = 135.148

Let us take a number which is closer to this

135

we can see that when we square the number

135,

(135)² = 18225

So according to this number if we want to make the given number a perfect square we have to subtract the number, but in the question we have to add the number to make it a perfect square.

So now we will find the square of the next nearest number i.e.

136 .

Upon squaring it gives us value

(136)2=18496 .

Now we subtract both these numbers i.e.

18496−18265=231 .

It means that if we add 231 to 18265 , then it will be a perfect square.

Hence the required answer is 231 .

So, the correct answer is “ 231 ”.

Note: We should note that to check whether the number is a perfect square, we can factorise the number and their prime numbers are paired in case of square. Then we can find their differences. As for example we can write the factors of 18225 i.e.

18225=3×3×3×3×3×3×5×5

Or it can be written as 18225=36×52

Here the prime factors are 3,5.