1. **State the problem:** Find the square root of $$\frac{(5 \times 10^{150}) - (1 \times 10^{149})}{4 \times 10^{23}}$$ and express the answer in standard form. 2. **Write the expression clearly:** $$\sqrt{\frac{5 \times 10^{150} - 1 \times 10^{149}}{4 \times 10^{23}}}$$ 3. **Simplify the numerator:** Factor out $$10^{149}$$ from the numerator: $$5 \times 10^{150} - 1 \times 10^{149} = 10^{149} (5 \times 10^{1} - 1) = 10^{149} (50 - 1) = 10^{149} \times 49$$ 4. **Rewrite the expression:** $$\sqrt{\frac{10^{149} \times 49}{4 \times 10^{23}}}$$ 5. **Simplify the fraction inside the square root:** $$\frac{10^{149} \times 49}{4 \times 10^{23}} = \frac{49}{4} \times 10^{149 - 23} = \frac{49}{4} \times 10^{126}$$ 6. **Take the square root:** $$\sqrt{\frac{49}{4} \times 10^{126}} = \sqrt{\frac{49}{4}} \times \sqrt{10^{126}} = \frac{7}{2} \times 10^{\frac{126}{2}} = \frac{7}{2} \times 10^{63}$$ 7. **Express the answer in standard form:** $$\frac{7}{2} = 3.5$$ So the final answer is: $$3.5 \times 10^{63}$$