Subjects algebra

Simplify Radical 29D7B7

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1. **State the problem:** Simplify the radical expression $$\sqrt{160}$$. 2. **Recall the formula and rules:** To simplify a square root, factor the number inside the radical into its prime factors or perfect squares. 3. **Factor 160:** $$160 = 16 \times 10$$ 4. **Use the property of radicals:** $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$ 5. **Apply to our factors:** $$\sqrt{160} = \sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10}$$ 6. **Simplify the perfect square:** $$\sqrt{16} = 4$$ 7. **Final simplified form:** $$\sqrt{160} = 4 \sqrt{10}$$ This means the square root of 160 can be expressed as 4 times the square root of 10, which is the simplest radical form.