Algebra Examples

$\sqrt{6 {(1 - \sqrt{5})}^{2}}$

Step 1

Rewrite $6 {(1 - \sqrt{5})}^{2}$ as ${(1^{2} - \sqrt{5})}^{2} \cdot 6$ .

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Step 1.1

Reorder $6$ and ${(1 - \sqrt{5})}^{2}$ .

$\sqrt{{(1 - \sqrt{5})}^{2} \cdot 6}$

Step 1.2

Rewrite $1$ as $1^{2}$ .

$\sqrt{{(1^{2} - \sqrt{5})}^{2} \cdot 6}$

Step 2

Pull terms out from under the radical.

$(1^{2} - \sqrt{5}) \sqrt{6}$

Step 3

One to any power is one.

$(1 - \sqrt{5}) \sqrt{6}$

Step 4

Apply the distributive property.

$1 \sqrt{6} - \sqrt{5} \sqrt{6}$

Step 5

Multiply $\sqrt{6}$ by $1$ .

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

Step 6

Multiply $- \sqrt{5} \sqrt{6}$ .

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Step 6.1

Combine using the product rule for radicals.

$\sqrt{6} - \sqrt{6 \cdot 5}$

Step 6.2

Multiply $6$ by $5$ .

$\sqrt{6} - \sqrt{30}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt{6} - \sqrt{30}$

Decimal Form:

$- 3.02773583 \dots$