Find the smallest six digit number which is a perfect square.
i need step by step explanation
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Answers
The least six-digit perfect square is 100489.
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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 =10000
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.
⇒ 10×1010−−√=10010−−√
Now, we will put the value of 10−−√ which is 3.1623
⇒ 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.
Step-by-step explanation: