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With a calculator, by trial and error, or maybe from a table.
For example, find the square root of 71 by trial and error:
First, find the perfect squares above and below 71:
82 = 64
?2 = 71
92 = 81
The square root of 71 is between 8 and 9, a little closer to 8.
Guess 8.4. Now 8.42 = 70.56, so 8.4 is a bit low (You can use a basic calculator to multiply, assume it doesn't have a square root key). Check 8.52 = 72.25 (1.25 high), 8.4 is much closer (-0.44).
Guess it is 8.43, 8.432 = 71.0649, high. Try 8.422 = 70.8964. 8.43 is closer so the square root of 71 is 8.43, correct to 2 decimals.
If you want, you can continue to get a more accurate value.
There are ways of getting the answer more quickly, but they are harder to understand. Newton's method is well known.
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Is the square root of 2 a real number?
Yes. In general, the square root of any non-negative number is a real number.
How many numbers does the square root have?
The number of digits in the square root of a number depends on the number. If it is a square number, the square root will have a finite number of digits. If the number is not a square number then the square root will be an irrational number with an infinite, non-repeating decimal representation. In both cases, the number of digits before the decimal point, in the square root of x will be the rounded value of 1+0.5*log10(x)
Is the square root of 257 an irrational number rational number o an whole number?
The square root of 257 is an irrational number, as it cannot be expressed as a fraction or whole number. It is a non-repeating, non-terminating decimal.
Is the square root of 112 a rational number?
Yes, because it is a non-perfect square
Can numbers that are not square have square roots?
Yes and no. It depends on your definition of square root. By the actual one, yes. All non-negative numbers have a square root. That square root might be irrational but it has a square root, nonetheless. 10 isn't a square number because there's no integer that can be squared to make ten but 10 definitely has a square root: 3.16227766....... If by square root you mean an integer square root, then no. If a number has an integer as its square root then you could square that integer to get the number, making it a square number.
