Fast square root extraction. Effective trick and its solution

EFFECTIVE FOCUSES AND THEIR CLUES
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Fast square root extraction. Focus secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

Focus Description:

Square roots are just as easy to calculate if a perfect square is given. For example, if someone told you that the square of a two-digit number is 7569, then you can instantly answer that the original number (square root) is 87.

Focus secret:

1. Look at the value of the hundreds (numbers preceding the last two) in this example.

2. Since 75 is between 82 (8² = 64) and 92 (9² = 81), then we know that the square root will be somewhere in the "80 plus" range. Therefore, its first digit is 8.

There are two numbers whose squares end in 9: 32 = 9, 72 = 49. So the last digit of the square root must be either 3 or 7. So the square root is either 83 or 87. Which one?

3. Compare the original number with the square of 85 (which can be easily calculated as 80 x 9 0 + 25 = 7225). Since 7569 is greater than 7225, the square root will be a larger number, i.e. 87.

Let's solve one more example. What is the square root of 4761? Since 47 lies between 62 = 36 and 72 = 49, the answer must be in the "60 plus" range. If the last digit of the square is 1, then the last digit of the square root must be 1 or 9. Since 4761 is greater than 652 = 4225, then the square root must be 69. As with the previous cube root trick, this method can only be used when the original number is a perfect square.

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