Subjects algebra

Sqrt5 Sum B2B360

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1. **State the problem:** Simplify the expression $\sqrt{5} + \sqrt{5} + \sqrt{5} + \sqrt{5} + \sqrt{5}$ and express it in the form $5^y$. 2. **Recall the formula and rules:** Adding the same terms is multiplication: $a + a + a + \dots = n \times a$. 3. **Simplify the sum:** There are 5 terms of $\sqrt{5}$, so $$\sqrt{5} + \sqrt{5} + \sqrt{5} + \sqrt{5} + \sqrt{5} = 5 \times \sqrt{5}$$ 4. **Rewrite $\sqrt{5}$ as an exponent:** $\sqrt{5} = 5^{\frac{1}{2}}$. 5. **Substitute and simplify:** $$5 \times 5^{\frac{1}{2}} = 5^{1} \times 5^{\frac{1}{2}} = 5^{1 + \frac{1}{2}} = 5^{\frac{3}{2}}$$ 6. **Final answer:** $$\sqrt{5} + \sqrt{5} + \sqrt{5} + \sqrt{5} + \sqrt{5} = 5^{\frac{3}{2}}$$