CUBE ROOT OF (0.027 / 0.008) PLUS SQUARE ROOT OF (0.09/0.04) – 1
The Correct Answer and Explanation is:
Let’s break down the given expression step by step and find the solution:
The expression is: 0.0270.0083+0.090.04−1\sqrt[3]{\frac{0.027}{0.008}} + \sqrt{\frac{0.09}{0.04}} – 130.0080.027+0.040.09−1
Step 1: Cube Root of 0.0270.008\frac{0.027}{0.008}0.0080.027
First, calculate 0.0270.008\frac{0.027}{0.008}0.0080.027: 0.0270.008=3.375\frac{0.027}{0.008} = 3.3750.0080.027=3.375
Now, find the cube root of 3.375: 3.3753=1.5\sqrt[3]{3.375} = 1.533.375=1.5
Step 2: Square Root of 0.090.04\frac{0.09}{0.04}0.040.09
Next, calculate 0.090.04\frac{0.09}{0.04}0.040.09: 0.090.04=2.25\frac{0.09}{0.04} = 2.250.040.09=2.25
Now, find the square root of 2.25: 2.25=1.5\sqrt{2.25} = 1.52.25=1.5
Step 3: Putting It All Together
Now substitute the results back into the original expression: 1.5+1.5−11.5 + 1.5 – 11.5+1.5−1 3.0−1=2.03.0 – 1 = 2.03.0−1=2.0
Final Answer: 2.0
Explanation:
To solve this problem, we needed to evaluate two types of roots: the cube root and the square root. These are basic operations in mathematics.
- Cube Root: The cube root of a number is the value that, when multiplied by itself three times, gives the original number. For example, the cube root of 3.375 is 1.5 because 1.5×1.5×1.5=3.3751.5 \times 1.5 \times 1.5 = 3.3751.5×1.5×1.5=3.375.
- Square Root: The square root of a number is the value that, when multiplied by itself, gives the original number. In our case, the square root of 2.25 is 1.5 because 1.5×1.5=2.251.5 \times 1.5 = 2.251.5×1.5=2.25.
- After evaluating both roots, we simply added and subtracted the results to get the final answer of 2.0. This shows how different mathematical operations can be combined in a single expression to arrive at a solution.
The importance of understanding how cube and square roots work is that these operations are fundamental in various fields of science and engineering, often used in solving equations involving growth, rates, and many other applications.
