In each of the following questions, find the exact value of (?)
`(sqrt(1521))/(sqrt(169)) xx (sqrt(1444))/(sqrt(361)) xx (10)^(2) = sqrt(100) xx ?`

Options

A. 40
B. 80
C. 70
D. 60

Answer

To solve the equation

\[ \frac{\sqrt{1521}}{\sqrt{169}} \times \frac{\sqrt{1444}}{\sqrt{361}} \times (10)^2 = \sqrt{100} \times ? \]

we will break it down step by step.

### Step 1: Simplify each square root
First, we will simplify the square roots in the expression.

- \(\sqrt{1521} = 39\) (since \(39^2 = 1521\))
- \(\sqrt{169} = 13\) (since \(13^2 = 169\))
- \(\sqrt{1444} = 38\) (since \(38^2 = 1444\))
- \(\sqrt{361} = 19\) (since \(19^2 = 361\))
- \(\sqrt{100} = 10\) (since \(10^2 = 100\))

### Step 2: Substitute the simplified values
Now we can substitute these values back into the equation:

\[ \frac{39}{13} \times \frac{38}{19} \times 10^2 = 10 \times ? \]

### Step 3: Calculate the left side
Now we will calculate the left side of the equation:

1. Calculate \(\frac{39}{13}\):
\[ \frac{39}{13} = 3 \]

2. Calculate \(\frac{38}{19}\):
\[ \frac{38}{19} = 2 \]

3. Now substitute these values back into the equation:
\[ 3 \times 2 \times 10^2 = 10 \times ? \]

4. Calculate \(10^2\):
\[ 10^2 = 100 \]

5. Now multiply:
\[ 3 \times 2 \times 100 = 600 \]

### Step 4: Set up the equation
Now we have:
\[ 600 = 10 \times ? \]

### Step 5: Solve for ?
To find the value of ?, we divide both sides by 10:
\[ ? = \frac{600}{10} = 60 \]

### Final Answer
Thus, the exact value of \( ? \) is \( 60 \).

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