1. The problem asks to find which expression is NOT equivalent to $\frac{\sqrt{136}}{\sqrt{2}}$. 2. Recall the property of square roots: $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$. 3. Apply this property to the original expression: $$\frac{\sqrt{136}}{\sqrt{2}} = \sqrt{\frac{136}{2}} = \sqrt{68}$$ 4. Check each option: - $\sqrt{\frac{136}{2}} = \sqrt{68}$ (equivalent) - $\sqrt{68}$ (equivalent) - $\frac{\sqrt{100 \times 1.36}}{\sqrt{2}}$ 5. Simplify $\sqrt{100 \times 1.36}$: $$\sqrt{100 \times 1.36} = \sqrt{136}$$ 6. So the third option is: $$\frac{\sqrt{136}}{\sqrt{2}} = \sqrt{68}$$ (equivalent) 7. The fourth option is $2 \sqrt{17}$. 8. Simplify $\sqrt{68}$: $$\sqrt{68} = \sqrt{4 \times 17} = \sqrt{4} \times \sqrt{17} = 2 \sqrt{17}$$ 9. So $2 \sqrt{17}$ is equivalent to $\sqrt{68}$. 10. All options except the third are equivalent to $\sqrt{68}$. 11. The third option is $\frac{\sqrt{100 \times 1.36}}{\sqrt{2}} = \frac{\sqrt{136}}{\sqrt{2}} = \sqrt{68}$, so it is also equivalent. 12. However, the third option is written as $\frac{\sqrt{100 \times 1.36}}{\sqrt{2}}$, which simplifies to $\sqrt{68}$, so it is equivalent. 13. Therefore, all options are equivalent to $\sqrt{68}$ except the third option if misinterpreted. 14. But since the third option simplifies correctly, all options are equivalent. 15. The problem asks for the expression NOT equivalent, so none of the given options is NOT equivalent. 16. Re-examining the third option carefully: $\frac{\sqrt{100 \times 1.36}}{\sqrt{2}} = \frac{\sqrt{136}}{\sqrt{2}} = \sqrt{68}$, so it is equivalent. 17. Therefore, all options are equivalent. 18. Since the problem asks to select the expression NOT equivalent, and all are equivalent, the answer is none. Final answer: None of the given expressions is NOT equivalent; all are equivalent to $\sqrt{68}$.