Page 43 - General_Knowledge_7

Mathemagic

Working With Square Roots:

A. The trick to working with square roots, is to know what range the square root is in. Since squaring
numbers ending in 0 and squaring numbers ending in 5 are both easy, we can get the answer within
a range of 5.
B. If the number is a perfect square, then we can know the ending digit of the answer by looking at
the ending digit of the question.
For example, if the number in question ends in a:

0 then the ending digit of answer is a 0
1 then the ending digit of answer is 1 or 9.
4 then the ending digit of answer is 2 or 8.

5 then the ending digit of answer is a 5.
6 then the ending digit of answer is 4 or 6.
9 then the ending digit of answer is 3 or 7.

C. After finding the last digit (or possibility between two digits), mentally remove the last two digits
and focus on the remaining digits.

D. Now, try to find a range of 5 that the number (in step c) is in. Once you do this you know the
answer using step B. First, find a range of 10, then find out if the answer is in the upper-half of the
range (i.e. ends in 5, 6, 7, 8, or 9) or if the answer is in the lower-half of the range (i.e. ends in 0, 1,
2, 3, or 4) by squaring the middle number (the number in the range that ends in 5).

For example 5329 = __________________.

a. We know the last number must be a 3 or 7.
b. Chopping off the last two numbers we need to focus on the remaining numbers or 53.
c. We know that 7 = 49 and 8 = 64 so since 53 is between these two numbers, the answer is
2
2
between 70 and 80.
d. Squaring 75 we get 5625. Since the original number is lower than this, we know the answer is
in the lower-half.
e. The answer is 73.

Try some :
a. 4096 = __________________.

b. 1369 = __________________.
c. 3136 = __________________.
d. 361 = __________________.

e. 676 = __________________.

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