Sagot :
The easiest way to find a square root is to use a calculator, but you can do it without one. Here’s one way, using 12 as an example of the squared number:Pick a number that when squared, comes close to (but is less than) the number whose square root you’re finding: 3 × 3 = 9. This is a better choice than 4: 4 × 4 = 16Divide the number you’re finding the square root of (12) by the number you squared (3) in step 1: 12 ÷ 3 = 4Average the closest square root (3) and the answer of step 2 (4): 3 + 4 = 7. 7 ÷ 2 = 3.5Square the average to see how close the number is to 12:3.5 × 3.5 = 12.25—Close, but not close enough!Repeat steps 2 and 3 until the number squared is very close to 12:Divide: 12 ÷ 3.5 = 3.43Average: 3.5 + 3.43 = 6.9356.935 ÷ 2 = 3.4653.465 × 3.465 = 12.006, close enough!
If x is a number, the square root of a number is derived from [tex]x ^{ \frac{1}{2} } [/tex]
1) Without using the calculator, it's not difficult to find the square root if you memorize the perfect square. This is possible with practice.
Example: 4 (2×2), 9 (3×3) , 16 (4×4), 25 (5×5), 36 (6×6), 49 (7×7)
2) If the the radicand is not a perfect square, try breaking it down to its factors, where one of the factors is a perfect square.
Example:
[tex] \sqrt{48} [/tex]
48 is not a perfect square
The factors of 48 are:
12 and 4
16 and 3
8 and 6
Among the set of factors, 16 and 3 are factors where a factor is a perfect square which is 16.
[tex] \sqrt{48} = \sqrt{(16)(3)} [/tex]
[tex] \sqrt{(16)(3)} =4 \sqrt{3} [/tex]
Therefore:
[tex] \sqrt{48} =4 \sqrt{3} [/tex]
3) If the radicand is a prime number, then the radical is in simplified form, unless you are instructed to get the square root using calculator.
4) If the radicand can not be factored in such a way that none of its factors is a perfect square, then the radical number is in simplified form, unless you are instructed to get the square root using the calculator.
5). If the radicand is a negative number, follow item number 2 above, but the factor that is not a perfect square is the negative factor; it is written as imaginary number "i".
Example:
[tex] \sqrt{-48} = \sqrt{(16)(-3)} [/tex]
[tex]4 \sqrt{-3} = 4 \sqrt{3} i[/tex]
1) Without using the calculator, it's not difficult to find the square root if you memorize the perfect square. This is possible with practice.
Example: 4 (2×2), 9 (3×3) , 16 (4×4), 25 (5×5), 36 (6×6), 49 (7×7)
2) If the the radicand is not a perfect square, try breaking it down to its factors, where one of the factors is a perfect square.
Example:
[tex] \sqrt{48} [/tex]
48 is not a perfect square
The factors of 48 are:
12 and 4
16 and 3
8 and 6
Among the set of factors, 16 and 3 are factors where a factor is a perfect square which is 16.
[tex] \sqrt{48} = \sqrt{(16)(3)} [/tex]
[tex] \sqrt{(16)(3)} =4 \sqrt{3} [/tex]
Therefore:
[tex] \sqrt{48} =4 \sqrt{3} [/tex]
3) If the radicand is a prime number, then the radical is in simplified form, unless you are instructed to get the square root using calculator.
4) If the radicand can not be factored in such a way that none of its factors is a perfect square, then the radical number is in simplified form, unless you are instructed to get the square root using the calculator.
5). If the radicand is a negative number, follow item number 2 above, but the factor that is not a perfect square is the negative factor; it is written as imaginary number "i".
Example:
[tex] \sqrt{-48} = \sqrt{(16)(-3)} [/tex]
[tex]4 \sqrt{-3} = 4 \sqrt{3} i[/tex]