Question

Find the value of 12 - 1 / (√2 + 1), given that √2 = 1.4142

Answer 1

To find the value, substitute the given value of sqrt(2), rationalize the denominator, and subtract the result from 12. Use arithmetic to calculate the final answer.

Step-by-step explanation:

To find the value of 12 minus the fraction, 1 over (square root of 2 plus 1), given square root of 2 equals 1.4142, we follow these steps:

1. First, substitute the given value of √2 into the expression.
2. We then simplify the expression in the denominator by rationalizing it: multiply both the numerator and the denominator by the conjugate of the denominator, which is (√2 - 1), to remove the square root.
3. The fraction becomes 1 ∗ (√2 - 1) / (√2 + 1) ∗ (√2 - 1).
4. Simplify the denominator using the difference of squares formula, (a + b)(a - b) = a² - b², leaving 1 over (2 - 1).
5. Finally, subtract the result from 12 to find the sought value.

Using a calculator for the arithmetic part after rationalization yields the final answer.