Question

Use tables of cubes and reciprocals only to evaluate
3/0.0671-cube root of 385.22

Answer 1

To evaluate the expression using tables of cubes and reciprocals, we will calculate each term separately and then subtract them from each other.

First, let's convert 0.0671 to its reciprocal using the reciprocal table.

Reciprocal of 0.0671 = 1 / 0.0671 = 14.912

Now, let's calculate the cube root of 385.22 using the cube table.

Cube root of 385.22 ≈ 7.741

Finally, substitute these values into the expression:

3/0.0671 - cube root of 385.22 ≈ 3 / 14.912 - 7.741

To subtract these two values, we can take the reciprocal of the cube:

3 / 14.912 - 7.741 ≈ 3 / 14.912 - 1 / 7.741

Now, finding the common denominator for these fractions:

3 / 14.912 - 1 / 7.741 = (3 * 7.741) / (14.912 * 7.741) - (1 * 14.912) / (7.741 * 14.912)

Simplifying the numerators:

(3 * 7.741) / (14.912 * 7.741) - (1 * 14.912) / (7.741 * 14.912) = 23.223 / 115.574192 - 14.912 / 115.574192

Subtracting the two fractions:

23.223 / 115.574192 - 14.912 / 115.574192 = (23.223 - 14.912) / 115.574192

Calculating the numerator:

23.223 - 14.912 = 8.311

Substituting this value into the expression:

(23.223 - 14.912) / 115.574192 ≈ 8.311 / 115.574192

Dividing the numerator by the denominator:

8.311 / 115.574192 ≈ 0.0719

Therefore, the value of the expression 3/0.0671 - cube root of 385.22 using tables of cubes and reciprocals is approximately 0.0719.