Algebra Examples

$\sqrt{\frac{3 (400)}{2}} - \sqrt{\frac{3 (256)}{2}}$

Step 1

Simplify each term.

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Step 1.1

Reduce the expression by cancelling the common factors.

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Step 1.1.1

Reduce the expression $\frac{3 (400)}{2}$ by cancelling the common factors.

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Step 1.1.1.1

Factor $2$ out of $3 (400)$ .

$\sqrt{\frac{2 (3 \cdot (200))}{2}} - \sqrt{\frac{3 (256)}{2}}$

Step 1.1.1.2

Factor $2$ out of $2$ .

$\sqrt{\frac{2 (3 \cdot (200))}{2 (1)}} - \sqrt{\frac{3 (256)}{2}}$

Step 1.1.1.3

Cancel the common factor.

$\sqrt{\frac{2 (3 \cdot (200))}{2 \cdot 1}} - \sqrt{\frac{3 (256)}{2}}$

Step 1.1.1.4

Rewrite the expression.

$\sqrt{\frac{3 \cdot (200)}{1}} - \sqrt{\frac{3 (256)}{2}}$

Step 1.1.2

Divide $3 \cdot (200)$ by $1$ .

$\sqrt{3 \cdot (200)} - \sqrt{\frac{3 (256)}{2}}$

Step 1.2

Multiply $3$ by $200$ .

$\sqrt{600} - \sqrt{\frac{3 (256)}{2}}$

Step 1.3

Rewrite $600$ as $10^{2} \cdot 6$ .

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Step 1.3.1

Factor $100$ out of $600$ .

$\sqrt{100 (6)} - \sqrt{\frac{3 (256)}{2}}$

Step 1.3.2

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 6} - \sqrt{\frac{3 (256)}{2}}$

Step 1.4

Pull terms out from under the radical.

$10 \sqrt{6} - \sqrt{\frac{3 (256)}{2}}$

Step 1.5

Reduce the expression by cancelling the common factors.

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Step 1.5.1

Reduce the expression $\frac{3 (256)}{2}$ by cancelling the common factors.

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Step 1.5.1.1

Factor $2$ out of $3 (256)$ .

$10 \sqrt{6} - \sqrt{\frac{2 (3 \cdot (128))}{2}}$

Step 1.5.1.2

Factor $2$ out of $2$ .

$10 \sqrt{6} - \sqrt{\frac{2 (3 \cdot (128))}{2 (1)}}$

Step 1.5.1.3

Cancel the common factor.

$10 \sqrt{6} - \sqrt{\frac{2 (3 \cdot (128))}{2 \cdot 1}}$

Step 1.5.1.4

Rewrite the expression.

$10 \sqrt{6} - \sqrt{\frac{3 \cdot (128)}{1}}$

Step 1.5.2

Divide $3 \cdot (128)$ by $1$ .

$10 \sqrt{6} - \sqrt{3 \cdot (128)}$

Step 1.6

Multiply $3$ by $128$ .

$10 \sqrt{6} - \sqrt{384}$

Step 1.7

Rewrite $384$ as $8^{2} \cdot 6$ .

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Step 1.7.1

Factor $64$ out of $384$ .

$10 \sqrt{6} - \sqrt{64 (6)}$

Step 1.7.2

Rewrite $64$ as $8^{2}$ .

$10 \sqrt{6} - \sqrt{8^{2} \cdot 6}$

Step 1.8

Pull terms out from under the radical.

$10 \sqrt{6} - (8 \sqrt{6})$

Step 1.9

Multiply $8$ by $- 1$ .

$10 \sqrt{6} - 8 \sqrt{6}$

Step 2

Subtract $8 \sqrt{6}$ from $10 \sqrt{6}$ .

$2 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{6}$

Decimal Form:

$4.89897948 \dots$