Test your quick math skills with this viral square root brain teaser!

2. Simplify the Denominator Radical

• Find the principal square root of 36:$$\sqrt{36} = 6 \quad (\text{since } 6 \times 6 = 36)$$

3. Perform the Final Division

• Divide the simplified numerator by the simplified denominator:$$\frac{12}{6} = 2$$

Radical Breakdown Table

Term in Expression	Original Radical Form	Simplified Value	Role in Expression
First Numerator Term	$\sqrt{81}$	$9$	Added to second numerator term
Second Numerator Term	$\sqrt{9}$	$3$	Added to first numerator term
Combined Numerator	$9 + 3$	$12$	Dividend (Top of fraction)
Denominator	$\sqrt{36}$	$6$	Divisor (Bottom of fraction)
Final Answer	$12 / 6$	$2$	Final Simplified Result

Order of Operations Rule for Fractions

When simplifying fractional expressions with operations in the numerator or denominator:

1. Group Numerator and Denominator: Treat the entire numerator and the entire denominator as if they are enclosed in parentheses:$$\frac{\sqrt{81} + \sqrt{9}}{\sqrt{36}} \equiv (\sqrt{81} + \sqrt{9}) \div (\sqrt{36})$$
2. Evaluate Radicals First: Calculate all exponents and radicals before applying basic addition or division.
3. Simplify Top and Bottom: Fully compute the numerator value ($12$) and denominator value ($6$).
4. Divide: Execute the division operation last to arrive at the final integer answer ($2$).

Conclusion

The answer to the square root apple puzzle is 2. By evaluating each square root ($\sqrt{81}=9$, $\sqrt{9}=3$, $\sqrt{36}=6$), the fraction simplifies to $12 / 6$, giving a final result of $2$.