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A simple strategy is the Newton Raphson method. See link for details.
Suppose to wish to find the square root of a number k.
Define f(x) = x2 - k
Let f'(x) = 2*x
Now start with some estimate for sqrt(k), say x0.
Then calculate x1 = x0 - f(x0)/f'(x0) as the next estimate.
Repeat, using xn+1 = xn - f(xn)/f'(xn).
The estimates will soon be very close to sqrt(k)
To illustrate:
Try sqrt(50) - which is approx 7.071068.
Even though you know the answer, start with a pretty feeble first estimate:
x0 = 10
Then x1 = 10 - (102 - 50)/(2*10) = 7.5
x3 is accurate to 4 decimal places and x4 to 11 dp.
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What are two strategies for estimating decimal products?
One strategy is estimating the factors the other i don't know
What is the square root of 2 square inches?
square inches do not have square roots only number have square roots.
What is the difference between perfect and nonperfect square roots?
Perfect square roots are square roots that have a whole number that can go into it perfectly. Nonperfect square roots are square roots that have decimal numbers going into it. Example: Perfect Square Root: 144- Square Root: 12 Nonperfect Square Root: 24- Square Root: About 4.89
What do you call nonnegative square roots?
You call them principal square roots.
What are square roots of 64?
The square roots of 64 are +8 and -8.
What are two strategies for estimating decimal products?
One strategy is estimating the factors the other i don't know
What is the square root of 11449?
The square roots are -1.07 and +1.07The square roots are -1.07 and +1.07The square roots are -1.07 and +1.07The square roots are -1.07 and +1.07
What is the square root of 2 square inches?
square inches do not have square roots only number have square roots.
What is the difference between perfect and nonperfect square roots?
Perfect square roots are square roots that have a whole number that can go into it perfectly. Nonperfect square roots are square roots that have decimal numbers going into it. Example: Perfect Square Root: 144- Square Root: 12 Nonperfect Square Root: 24- Square Root: About 4.89
What is the square root of 169 196?
169 and 196 are perfect squares. Their square roots are 13 and 14 respectively. The perfect squares from 1^2 to 16^2 are: 1,4, 9, 16, 25, 36, 49, 64, 81, 100, 144, 169, 196, 225, 256. It is useful to memorize the perfect squares, as it makes estimating square roots easier. In case you wanted to find the square root of 169,196, the answer is roughly 411.334414... The square roots of integers which are not perfect squares are irrational, so they can not be expressed exactly as a sequence of digits.
Are all square roots of even numbers rational?
No. The square roots 8 are irrational, as are the square roots of most even numbers.
What are square roots of 64?
The square roots of 64 are +8 and -8.
What do you call nonnegative square roots?
You call them principal square roots.
What are the square roots of 8100?
The square roots of 8100 are 90, -90
How are positive square roots different?
The answer depends on "different from WHAT?" Positive cube roots, or negative square roots?
What keeps a square from moving?
Concrete.
What the square roots of -256?
There are no real square roots of -256. But using complex numbers the square roots of -256 are 16i and -16i.
