Evaluate 22.5^1/3 × 33.5/5√0.00523
To evaluate this expression, we will simplify it step by step.
First, let's simplify 22.5^(1/3). This means taking the cube root of 22.5.
The cube root of 22.5 is approximately 2.84387.
Next, let's simplify 33.5/(5√0.00523).
The square root of 0.00523 is approximately 0.07225216.
Then, multiplying 5 by √0.00523 gives us 5 * 0.07225216 = 0.3612608.
Finally, dividing 33.5 by 0.3612608 gives us approximately 92.732926.
So, 22.5^(1/3) × 33.5/(5√0.00523) is approximately:
2.84387 * 92.732926 ≈ 263.35537
To evaluate the expression, let's break it down step-by-step:
Step 1: Simplify the first term, 22.5^(1/3):
To simplify this term, we need to find the cube root of 22.5. Taking the cube root of 22.5 equals approximately 2.8439.
Step 2: Simplify the second term, 33.5 / 5√0.00523:
To simplify this term, we need to calculate the value of 5√0.00523 first. Taking the fifth root of 0.00523 equals approximately 0.2071, so 5√0.00523 simplifies to 0.2071.
Now we can calculate the value of the fraction: 33.5 / 0.2071 = 162.1107.
Step 3: Multiply the two simplified terms:
Now, we multiply the simplified terms together:
2.8439 * 162.1107 = 461.8559.
So, evaluating the expression 22.5^(1/3) * 33.5/5√0.00523 equals approximately 461.8559.