[tex]$\sqrt{5}+\sqrt[3]{70}$[/tex]
Answer (1)
Approximate 5 which is approximately 2.236 .
Approximate 3 70 which is approximately 4.121 .
Add the two approximations: 2.236 + 4.121 = 6.357 .
The final result is 6.357 .
Explanation
Understanding the Expression We are given the expression 5 + 3 70 . Our goal is to evaluate this expression. Since 5 and 70 do not share any common factors, we cannot simplify the radicals. Therefore, we will approximate the value of each term and then add them together.
Approximating the Square Root First, we approximate 5 . The result is approximately 2.236.
Approximating the Cube Root Next, we approximate 3 70 . The result is approximately 4.121.
Adding the Approximations Now, we add the two approximations together: 2.236 + 4.121 = 6.357 .
Final Result Therefore, 5 + 3 70 ≈ 6.357 .
Examples
Imagine you are building a garden and need to calculate the total length of two different types of decorative borders. One border requires 5 meters of material, and the other requires 3 70 meters. By adding these two values, you can determine the total amount of material needed for both borders. This helps in planning and purchasing the correct amount of materials for your gardening project. This problem demonstrates how adding radicals can be useful in real-world measurement and planning scenarios.
