Learn how to mentally calculate square roots and amaze your friends!

Calculating square roots is rather more difficult than either cube roots or fifth roots - you might want to learn these two methods first.

Following a few simple steps you will be able to instantly calculate the

square rootof the spectator's number.

To perform this, you should ask the spectator to choose

any whole number less than 100and, using a calculator, to square it by multiplying the number by itself.

The spectator then calls out the answer, and you instantly reveal the original number (i.e., the square root).

Note that this method will NOT work with non-whole numbers, or with numbers greater than 99.

To master the system you must

learn by heartthe squares of numbers 0 to 9, which are shown in the table below. You also need to consider the last digit of each square.

Number Square Last Digit 0 0 0 1 1 1 2 4 4 3 9 9 4 16 6 5 25 5 6 36 6 7 49 9 8 64 4 9 81 1 Note how the last digits for the squares

of 1 and 9 are both 1.

Note how the last digits for the squares

of 2 and 8 are both 4.

Note how the last digits for the squares

of 3 and 7 are both 9.

Note how the last digits for the squares

of 4 and 6 are both 6.

Ignore the last TWOdigits of the number called out by the spectator and choose the memorizedcomparison SQUARE valuewhich isjust lower (or equal)to the remaining number. The corresponding square root of this is thefirst digit. of your answer

## Example 1

Spectator calls 676

- Ignore 76, leaving 6
- The comparison square value which is
just lowerthan 6 is 4- Therefore the first digit of the answer is the square root of 4 = 2

## Example 2

Spectator calls 5184

- Ignore 84, leaving 51
- The comparison square value which is
just lowerthan 51 is 49- Therefore the first digit of the answer is the square root of 49 = 7

Now consider the

last digitof the number called out by the spectator and compare this to the last digit of the memorized squares.

- If the last digit of the spectator's call is 0, then the last digit of your answer is also 0.
- If the last digit of the spectator's call is 5, then the last digit of your answer is 5.
- In all other cases, the last digit of the spectator's call will indicate
two possible valuesfor the last digit of the square root. For example, if the last digit of the spectator's call is 9, then the square root may end in either 3 or 7.

To determine whether the lower or higher of two possible values should be taken, multiply the

first digitof your answer (as found in Step 2) byone greater than itself.

- If this is
greater than(i.e., ignoring the last two digits), then the last digit of your answer is thelowerof the two possible values.- If this is
less than (or equal to)the first part of the number called by the spectator, then the last digit of your answer is thehighervalue.

## Example 1

Spectator calls 676

- Last digit of spectator's call = 6
- Therefore the two possible values of the second digit are 4 or 6
- First digit of answer (from Step 2) is 2
- Multiply 2 by (2+1) = 6
- Because 6 is
equal tothe first part of the spectator's call (6), then the second digit will be thehigherof the two possible values- Therefore the second digit is 6 (not 4)
- Therefore the square root of 676 is 26

## Example 2

Spectator calls 5184

- Last digit of spectator's call = 4
- Therefore the two possible values of the second digit are 2 or 8
- First digit of answer (from Step 2) is 7
- Multiply 7 by (7+1) = 56
- Because 56 is
greater thanthe first part of the spectator's call (51), then the second digit will be thelowerof the two possible values- Therefore the second digit is 2 (not 8)
- Therefore the square root of 5184 is 72

## Further Examples

Call

SQ1st

Part

(P)Lower

(or =)

SQ1st

Digit

(F)2nd

Digit?F x

(F+1)Compare

with P2nd

Digit

(S)SQRT

= FS144 1 1 1 2 or 8 2 2 > 1 2 12 784 7 4 2 2 or 8 6 6 < 7 8 28 1369 13 9 3 3 or 7 12 12 < 13 7 37 2025 20 16 4 5 5 45 2401 24 16 4 1 or 9 20 20 < 24 9 49 2809 28 25 5 3 or 7 30 30 > 28 3 53 3600 36 36 6 0 0 60 5041 50 49 7 1 or 9 56 56 > 50 1 71 7396 73 64 8 4 or 6 72 72 < 73 6 86 8836 88 81 9 4 or 6 90 90 > 88 4 94

Before you try this out on your friends, you should practice until you can calculate the square root instantly and without error.

If you can't do this, then

practice some more!

To practice and assess your ability, you can use the Square Root Tester shown below.

## Square Root Tester

## by Psychic Science

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