Solving the Math Expression with Square Roots

The problem requires calculating the value of the given mathematical expression involving square roots of decimals.

The expression is: $ \frac{3}{\sqrt{0.0009}} + \frac{4}{\sqrt{0.0016}} $

Step 1: Calculate the Square Roots

• First, find the square root of $0.0009$. Note that $0.0009 = \frac{9}{10000}$. $ \sqrt{0.0009} = \sqrt{\frac{9}{10000}} = \frac{\sqrt{9}}{\sqrt{10000}} = \frac{3}{100} = 0.03 $
• Next, find the square root of $0.0016$. Note that $0.0016 = \frac{16}{10000}$. $ \sqrt{0.0016} = \sqrt{\frac{16}{10000}} = \frac{\sqrt{16}}{\sqrt{10000}} = \frac{4}{100} = 0.04 $

Step 2: Substitute and Simplify the Expression

Substitute the calculated square root values back into the original expression:

Now, simplify each term:

• $ \frac{3}{0.03} = \frac{3}{3/100} = 3 \times \frac{100}{3} = 100 $
• $ \frac{4}{0.04} = \frac{4}{4/100} = 4 \times \frac{100}{4} = 100 $

Step 3: Final Calculation

Add the results from the simplified terms:

Therefore, the value of the expression is $200$.