\(\sqrt{29.8116}+\sqrt{77.44}=\)
14.26
Solving the Square Root Sum Equation
This problem requires us to find the sum of two square roots: $ \sqrt{29.8116} $ and $ \sqrt{77.44} $. We will calculate each square root separately and then add them together.
Step 1: Calculate the Square Root of 29.8116
We need to find the value of $ \sqrt{29.8116} $. Let's determine this value.
- We can estimate the value: $ 5^2 = 25 $ and $ 6^2 = 36 $. So, the square root is between 5 and 6.
- Testing values, we find that $ 5.46 \times 5.46 = 29.8116 $.
Therefore, $ \sqrt{29.8116} = 5.46 $.
Step 2: Calculate the Square Root of 77.44
Next, we need to find the value of $ \sqrt{77.44} $.
- We can estimate this value: $ 8^2 = 64 $ and $ 9^2 = 81 $. So, the square root is between 8 and 9.
- Testing values, we find that $ 8.8 \times 8.8 = 77.44 $.
Therefore, $ \sqrt{77.44} = 8.8 $.
Step 3: Sum the Calculated Square Roots
Now, we add the results from Step 1 and Step 2:
Sum = $ \sqrt{29.8116} + \sqrt{77.44} $
Sum = $ 5.46 + 8.8 $
Sum = $ 14.26 $
Step 4: Match the Result with the Options
The calculated sum is $ 14.26 $. Comparing this value with the given options:
- Option 1: 12.62
- Option 2: 12.26
- Option 3: 14.26
- Option 4: 14.62
Our calculated result $ 14.26 $ matches Option 3.
Important Questions from Surds and Indices
The value of (0.3) [{(200 - 146)/(3 × 3 × 3)} - 3] is:
The expression \(\frac{{15\left( {\sqrt {10} + \sqrt 5 } \right)}}{{\sqrt {10\;} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}\) is equal to:
Let \(x = \left( {\frac{{√ {1875} }}{{√ {3888} }} \div \frac{{√ {1200} }}{{\sqrt 768}}} \right) \times \frac{{√ {175} }}{{√ {1792} }}\) . Then √x is equal to:
If \(x = \sqrt {-\sqrt 3 + \sqrt {3 + 8\sqrt {7 + 4\sqrt 3}}}\) where x > 0, then the value of x is equal to:
What is the value of \(\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}−\sqrt{5}} \div \frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}−\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}\) ?
