Solve réel (- 2sqrt(5) - 3) ^ 2 est ég | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$( - 2 \sqrt { 5 } - 3 ) ^ { 2 }$$

Evaluate

$12\sqrt{5}+29\approx 55.83281573$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(-2\sqrt{5}-3\right)^{2}$.

$$4\left(\sqrt{5}\right)^{2}+12\sqrt{5}+9$$

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

$$4\times 5+12\sqrt{5}+9$$

Multiply $4$ and $5$ to get $20$.

$$20+12\sqrt{5}+9$$

Add $20$ and $9$ to get $29$.

$$29+12\sqrt{5}$$

Expand

$12 \sqrt{5} + 29 = 55.83281573$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(-2\sqrt{5}-3\right)^{2}$.

$$4\left(\sqrt{5}\right)^{2}+12\sqrt{5}+9$$

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

$$4\times 5+12\sqrt{5}+9$$

Multiply $4$ and $5$ to get $20$.

$$20+12\sqrt{5}+9$$

Add $20$ and $9$ to get $29$.

$$29+12\sqrt{5}$$