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One way to find the square root of a number is an iterative method. This entails making a guess at the answer and then improving on it. Repeating the procedure should lead to a better estimate at each stage. One such is the Newton-Raphson method.
If you want to find the square root of q, define f(x) = x2 - q.
Then finding the square root of kkk is equivalent to solving f(x) = 0.
Let f'(x) = 2x. This is the derivative of f(x) but you do not need to know that to use the N-R method.
Start with x0 as the first guess.
Then let xn+1 = xn - f(xn)/f'(xn) for n = 0, 1, 2, …
Provided you made a reasonable choice for the starting point, the iteration will very quickly converge to the true answer. Even if your first guess is not so good:
Depending on your arithmetical skills, this method may require a calculator and, if you do have a calculator available, you may be able to use it to find the square root!
Another way is bracketing.
If you want the square root of k, find two rational numbers a and b such that
a2 < k2 < b2. Then find rational numbers between a and k and between k and b so that a similar relationship holds. You will gradually narrow the possible range for k.
What else can I help you with?
Is the square root of a irrational number always rational?
No, the square root of an irrational number is not always rational. In fact, the square root of an irrational number is typically also irrational. For example, the square root of 2, which is an irrational number, is itself irrational. However, there are exceptions, such as the square root of a perfect square of an irrational number, which can be rational.
Is the square root of 7 irrational or rational?
It is a irrational number. Because the square root of every imperfect square is irrational number.
Can multiplying two irrational numbers give you an irrational number?
Yes. For example, the square root of 3 (an irrational number) times the square root of 2(an irrational number) gets you the square root of 6(an irrational number)
Is the square root of 26 a rational number or irrational number?
the square root of 26 is a irrational number
Is the square root of 47 a irrational or rational number?
The square root of 47 is an irrational number.
Is the square root of a irrational number always rational?
No, the square root of an irrational number is not always rational. In fact, the square root of an irrational number is typically also irrational. For example, the square root of 2, which is an irrational number, is itself irrational. However, there are exceptions, such as the square root of a perfect square of an irrational number, which can be rational.
Is the square root of 7 irrational or rational?
It is a irrational number. Because the square root of every imperfect square is irrational number.
How do you find an irrational square root?
An irrational number is a number that never ends. An example of an irrational square root would be the square root of 11.
Is the square root of 27 a rational or irrational number?
The square root of 27 is an irrational number
Can multiplying two irrational numbers give you an irrational number?
Yes. For example, the square root of 3 (an irrational number) times the square root of 2(an irrational number) gets you the square root of 6(an irrational number)
Is the square root of 26 a rational number or irrational number?
the square root of 26 is a irrational number
Is they sqare root of 94 irrational or irrational?
The square root of 94 is an irrational number
Is the square root of 121 an irrational number?
The square root of 121 is 11 which is not an irrational number.
Is the square root a 2 an irrational number?
Yes, the square root of 2 is an irrational number.
Is the square root of 47 a irrational or rational number?
The square root of 47 is an irrational number.
Is the square root of nine an irrational number?
The square root of nine is three, and that is not an irrational number.
Is the square root of 71 a rational number or irrational?
The square root of 71 is an irrational number
