Solve 2sqrt(6) * (3sqrt(2) - 2sqrt(5)) | 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

$$2\sqrt{6}(3\sqrt{2}-2\sqrt{5})$$

Evaluate

$4\left(3\sqrt{3}-\sqrt{30}\right)\approx -1.124292609$

Solution Steps

Use the distributive property to multiply $2\sqrt{6}$ by $3\sqrt{2}-2\sqrt{5}$.

$$6\sqrt{6}\sqrt{2}-4\sqrt{6}\sqrt{5}$$

Factor $6=2\times 3$. Rewrite the square root of the product $\sqrt{2\times 3}$ as the product of square roots $\sqrt{2}\sqrt{3}$.

$$6\sqrt{2}\sqrt{3}\sqrt{2}-4\sqrt{6}\sqrt{5}$$

Multiply $\sqrt{2}$ and $\sqrt{2}$ to get $2$.

$$6\times 2\sqrt{3}-4\sqrt{6}\sqrt{5}$$

Multiply $6$ and $2$ to get $12$.

$$12\sqrt{3}-4\sqrt{6}\sqrt{5}$$

To multiply $\sqrt{6}$ and $\sqrt{5}$, multiply the numbers under the square root.

$$12\sqrt{3}-4\sqrt{30}$$