Question

$\sqrt{15612 + \sqrt{154 + \sqrt{225}} }$

• A. 81
• B. 100
• C. 125
• D. 144

Answer 1

Answer:

C. 125

To solve this nested square root expression, we work from the innermost square root outward:

$\sqrt{15612 + \sqrt{154 + \sqrt{225}} }$

Step 1: Solve the innermost square root

We know that $\sqrt{225} = 15$. Substitute this back into the expression:
$\sqrt{15612 + \sqrt{154 + 15} }$

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Step 2: Simplify the middle addition

Add the numbers inside the middle square root:
$154 + 15 = 169$
The expression now looks like this:
$\sqrt{15612 + \sqrt{169} }$

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Step 3: Solve the middle square root

We know that $\sqrt{169} = 13$. Substitute this back into the expression:
$\sqrt{15612 + 13}$

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Step 4: Simplify the final addition

Add the numbers inside the outermost square root:
$15612 + 13 = 15625$
The expression is now:
$\sqrt{15625}$

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Step 5: Find the final square root

Find the square root of 15625:
$125 \times 125 = 15625 \implies \sqrt{15625} = \mathbf{125}$

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Final Answer

The value of the expression is 125.