How to solve sqrt(9+sqrt(9))

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

$$\sqrt{ 9+ \sqrt{ 9 } }$$

Evaluate

$2\sqrt{3}\approx 3.464101615$

Solution Steps

Calculate the square root of $9$ and get $3$.

$$\sqrt{9+3}$$

Add $9$ and $3$ to get $12$.

$$\sqrt{12}$$

Factor $12=2^{2}\times 3$. Rewrite the square root of the product $\sqrt{2^{2}\times 3}$ as the product of square roots $\sqrt{2^{2}}\sqrt{3}$. Take the square root of $2^{2}$.

$$2\sqrt{3}$$

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