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.
Yes. In general, the square root of any non-negative number is a real number.
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)
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.
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.
Yes, because it is a non-perfect square
Sometimes the square root of a positive number can be irrational, as in the square root of 2 (which is a non-perfect square number), but sometimes it is a rational number, as in the square root of 25 (which is a perfect square number).
You get an irrational number as the square root.
A banana is a non-example of a square root.In mathematics, every number is a square root of some number and so the question makes no sense.
Actually, as a non-integer square root of a number, 82 is an irrational number. It has no end.
Yes. In general, the square root of any non-negative number is a real number.
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)
Well . . there is not even such a thing as the square root of -6, unless you are working with non-real numbers. The square root of + 6, though, is not a whole number.
The square root of 61 is an irrational 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.
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.
Yes, because it is a non-perfect square
Square them both, find a non-square integer between those two results, and then take the square root of that number. In other words, find a non-square integer between 25 and 49, and since there is only one square number between them, 36, that should be easy; let's pick 42, and then take the square root of it. Ta da! √42 is an irrational number between 5 and 7, its first 30 digits being 6.48074069840786023096596743608.