What is the value of `sqrt(513-sqrt(144)-sqrt(81)-sqrt(64))` ?

Options

A. 22
B. 21
C. 28
D. 19

Answer

To solve the expression \( \sqrt{513 - \sqrt{144} - \sqrt{81} - \sqrt{64}} \), we will follow these steps:

### Step 1: Calculate the square roots of the numbers inside the expression.
- \( \sqrt{144} = 12 \)
- \( \sqrt{81} = 9 \)
- \( \sqrt{64} = 8 \)

### Step 2: Substitute the square roots back into the expression.
Now we can rewrite the expression:
\[ \sqrt{513 - 12 - 9 - 8} \]

### Step 3: Perform the subtraction inside the square root.
First, we will subtract \( 12 \), \( 9 \), and \( 8 \) from \( 513 \):
\[ 12 + 9 + 8 = 29 \]
Now, subtract \( 29 \) from \( 513 \):
\[ 513 - 29 = 484 \]

### Step 4: Take the square root of the result.
Now we need to find \( \sqrt{484} \):
\[ \sqrt{484} = 22 \]

### Final Answer:
Thus, the value of \( \sqrt{513 - \sqrt{144} - \sqrt{81} - \sqrt{64}} \) is \( 22 \).

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