if `sqrtroot3(x xx 0.000009)=0.3` ,then the value of `sqrtx` is

Options

A. 27
B. 81
C. 9
D. 18

Answer

To solve the equation \( \sqrt[3]{x \times 0.000009} = 0.3 \), we will follow these steps:

### Step 1: Write the given equation
We start with the equation:
\[ \sqrt[3]{x \times 0.000009} = 0.3 \]

### Step 2: Square both sides
To eliminate the cube root, we will cube both sides of the equation:
\[ x \times 0.000009 = (0.3)^3 \]

### Step 3: Calculate \( (0.3)^3 \)
Calculating \( (0.3)^3 \):
\[ (0.3)^3 = 0.3 \times 0.3 \times 0.3 = 0.027 \]
So we have:
\[ x \times 0.000009 = 0.027 \]

### Step 4: Solve for \( x \)
Now, we will isolate \( x \) by dividing both sides by \( 0.000009 \):
\[ x = \frac{0.027}{0.000009} \]

### Step 5: Simplify the fraction
To simplify \( \frac{0.027}{0.000009} \), we can multiply the numerator and the denominator by \( 1000000 \) (to eliminate the decimals):
\[ x = \frac{0.027 \times 1000000}{0.000009 \times 1000000} = \frac{27000}{9} \]
Calculating \( \frac{27000}{9} \):
\[ x = 3000 \]

### Step 6: Find \( \sqrt{x} \)
Now we need to find \( \sqrt{x} \):
\[ \sqrt{x} = \sqrt{3000} \]

### Step 7: Simplify \( \sqrt{3000} \)
We can simplify \( \sqrt{3000} \):
\[ \sqrt{3000} = \sqrt{300 \times 10} = \sqrt{300} \times \sqrt{10} \]
Breaking down \( \sqrt{300} \):
\[ \sqrt{300} = \sqrt{100 \times 3} = 10\sqrt{3} \]
Thus:
\[ \sqrt{3000} = 10\sqrt{3} \times \sqrt{10} = 10\sqrt{30} \]

### Final Answer
So, the value of \( \sqrt{x} \) is:
\[ \sqrt{x} = 10\sqrt{30} \]

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