Question

how to estimate the value of square roots and cube roots​

Answer 1

Answer:

nice question

for estimating you need to take that function as f(x) and use the formula in errors and take that change as dx and proceed ur process

Answer 2

Answer:

Estimating square root of a number

For estimating the number of digits in the square root of a number, we use method of bars. For example:

961−−−√ = 31 and 1369−−−−√ = 37

The bar is placed on pair of digits starting from the rightmost digit.

9¯¯¯61¯¯¯¯¯and13¯¯¯¯¯69¯¯¯¯¯

In both the numbers above, we have 2 bars, that means, their square root will have two digits.

In order to estimate the square root of a number, consider the following example:

The number whose square root is to be determined = 247

Since: 100 < 247 < 400, and 100−−−√2 = 10 and 400−−−√2 = 20.

Taking the square root we get: 10 < 247−−−√2 < 20

We are not very close to the number yet.

We also know that 152 = 225 and 162 = 256, therefore 15 < 247−−−√2 < 16

The number 247 is much closer to 256 than 225.

Hence 247−−−√2 is approximately equal to 16.

Step-by-step explanation:

Estimating the cube root of a cube number

If a large number is given and stated that it is a perfect cube then we can use the following method to calculate its cube root by the method of estimation.

1. Take any cube number such as 29791 whose cube root is to be determined and start making a group of three digits starting from the rightmost digit.

2. The first group will give us the unit’s digit of the required cube root. The number 791 ends in 1, therefore, the last digit will be 1 because unit’s digit is 1 only when the cube root also ends with 1.

3. Now taking the second group, it is between 33 = 27 and 43 = 64. We take the smaller value, therefore, the digit at the tenths place is 3.

The required cube root of 29791 = 29791−−−−−√3 = 31.

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