Subjects algebra

Simplify Root Expression B6E4Ab

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Question: (top-left) $\sqrt{49} + \sqrt{\sqrt{81}}$ (top-left) $\frac{\text{above}}{\sqrt{4}}$ (center)
1. **State the problem:** Simplify the expression $$\frac{\sqrt{49} + \sqrt{\sqrt{81}}}{\sqrt{4}}$$. 2. **Recall important formulas and rules:** - The square root of a number $a$ is written as $\sqrt{a}$. - The square root of a square root can be written as $\sqrt{\sqrt{a}} = a^{1/4}$. - Simplify numerator and denominator separately before dividing. 3. **Simplify each term:** - $\sqrt{49} = 7$ - $\sqrt{81} = 9$, so $\sqrt{\sqrt{81}} = \sqrt{9} = 3$ - $\sqrt{4} = 2$ 4. **Substitute back:** $$\frac{7 + 3}{2}$$ 5. **Add numerator:** $$\frac{10}{2}$$ 6. **Simplify fraction:** $$\frac{\cancel{10}^{5}}{\cancel{2}^{1}} = 5$$ **Final answer:** $5$