Question

please solve this woth explanation​

Answer 1

Answer:

100489

Step-by-step explanation:

First, find the smallest six-digit number. Then find its square-root. When you obtain a square-root, check whether the square-root is an integer or not. If it is not an integer then find the nearest integer to the square-root that is greater than the square-root itself. You’ll have the required answer.

Complete step-by-step answer:

Here, we have to find the least six-digit number which is a perfect square.

So first we will find the least six-digit number or smallest six-digit number.

The smallest six digit number =100000

Now, we will find the square-root of this smallest six-digit number to determine whether the square-root is an integer or not.

⇒ 100000=√(10×10×10×10×10)

The numbers which are in pairs are removed from under the square-root as they are perfect squares.

⇒ 10×10√10=100√10

Now, we will put the value of √10 which is 3.162

⇒ 100×3.1623=316.23

The square-root we obtained is not an integer as it is in decimal.

So we have to find the nearest integer which is greater than the square-root itself.

So, the nearest integer 316.23 is 317 which is greater than the obtained square-root. Now, to find the perfect square we will multiply 317by itself.

⇒ 317×317=100489

⇒317×317=100489

The least six-digit perfect square is 100489.

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