8
Evaluate: 5−449⎯⎯⎯⎯√
1000
To evaluate the expression 5−449⎯⎯⎯⎯√, we start by taking the square root of 449:
√449 = 21.1897 (rounded to four decimal places)
Now, we can substitute this value back into the original expression:
5 - 21.1897 ≈ -16.1897
Therefore, 5−449⎯⎯⎯⎯√ is approximately -16.1897.
To evaluate the expression 5 - 4^(49/1000), we need to follow these steps:
Step 1: Simplify the exponent.
49/1000 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1. After simplification, we get 49/1000.
Step 2: Calculate the value of the exponent.
To calculate 4^(49/1000), we can take the 1000th root of 4 and then raise it to the power of 49. So, 4^(49/1000) = (4^(1/1000))^49.
Step 3: Calculate the 1000th root of 4.
To find the 1000th root of 4, we can use a calculator or estimate it. Using a calculator, we get the 1000th root of 4 to be approximately 1.000398.
Step 4: Raise the value obtained in Step 3 to the power of 49.
(1.000398)^49 can also be calculated using a calculator. The result is approximately 1.01988.
Step 5: Calculate 5 minus the value obtained in Step 4.
5 - 1.01988 = 3.98012.
Therefore, the value of the expression 5 - 4^(49/1000) is approximately 3.98012.
To evaluate the expression 5 - √(49 / 1000), follow these steps:
Step 1: Simplify the numerator.
49 ÷ 1000 = 0.049
Step 2: Take the square root.
√0.049 ≈ 0.2219 (rounded to four decimal places)
Step 3: Subtract from 5.
5 - 0.2219 ≈ 4.7781 (rounded to four decimal places)
Therefore, the value of the expression 5 - √(49 / 1000) is approximately 4.7781.