How to solve (sqrt(5)+2)^(2)

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.

Solve (sqrt(5)+2)^(2) | Equatix

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a⋅(b-2)=3b

3(r+2s)=2t-4

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Question

$${ \left( \sqrt{ 5 } +2 \right) }^{ 2 }$$

Evaluate

$4\sqrt{5}+9\approx 17.94427191$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(\sqrt{5}+2\right)^{2}$.

$$\left(\sqrt{5}\right)^{2}+4\sqrt{5}+4$$

The square of $\sqrt{5}$ is $5$.

$$5+4\sqrt{5}+4$$

Add $5$ and $4$ to get $9$.

$$9+4\sqrt{5}$$

Show Solution

Expand

$4 \sqrt{5} + 9 = 17.94427191$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(\sqrt{5}+2\right)^{2}$.

$$\left(\sqrt{5}\right)^{2}+4\sqrt{5}+4$$

The square of $\sqrt{5}$ is $5$.

$$5+4\sqrt{5}+4$$

Add $5$ and $4$ to get $9$.

$$9+4\sqrt{5}$$

Show Solution

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Solution Steps