The value of `sqrt(0.00001225/(0.00005329))-root3(sqrt0.000064)` is

Options

A. 0.2
B. 0.279
C. 0.479
D. 0

Answer

To solve the expression \( \sqrt{\frac{0.00001225}{0.00005329}} - \sqrt[3]{\sqrt{0.000064}} \), we will break it down step by step.

### Step 1: Simplify the square root expression
We start with the expression:

\[ \sqrt{\frac{0.00001225}{0.00005329}} \]

To simplify this, we can first divide the two numbers inside the square root.

### Step 2: Perform the division
Calculating the division:

\[ \frac{0.00001225}{0.00005329} = \frac{1225}{5329} \]

Now, we can calculate the square root of this fraction.

### Step 3: Calculate the square root
Next, we find the square root:

\[ \sqrt{\frac{1225}{5329}} = \frac{\sqrt{1225}}{\sqrt{5329}} = \frac{35}{73} \]

### Step 4: Simplify the cube root expression
Now, we will simplify the second part of the expression:

\[ \sqrt[3]{\sqrt{0.000064}} \]

First, we find the square root of \(0.000064\):

\[ \sqrt{0.000064} = 0.008 \]

### Step 5: Calculate the cube root
Now, we find the cube root of \(0.008\):

\[ \sqrt[3]{0.008} = 0.002 \]

### Step 6: Combine the results
Now we can combine the results from Step 3 and Step 5:

\[ \frac{35}{73} - 0.002 \]

### Step 7: Convert \(0.002\) to a fraction
To perform the subtraction, we need a common denominator. We can convert \(0.002\) to a fraction:

\[ 0.002 = \frac{2}{1000} = \frac{2}{1000} \cdot \frac{73}{73} = \frac{146}{73000} \]

### Step 8: Perform the subtraction
Now we perform the subtraction:

\[ \frac{35}{73} - \frac{146}{73000} \]

To subtract these fractions, we need to convert \(\frac{35}{73}\) to have the same denominator:

\[ \frac{35 \cdot 1000}{73 \cdot 1000} = \frac{35000}{73000} \]

Now we can subtract:

\[ \frac{35000 - 146}{73000} = \frac{34854}{73000} \]

### Final Result
Thus, the final result is:

\[ \frac{34854}{73000} \]