Basic Math Examples

$(\frac{- \sqrt{39}}{8}) (\frac{- \sqrt{7}}{4}) + (\frac{- \sqrt{7}}{4}) (\frac{- \sqrt{39}}{8})$

Step 1

Simplify each term.

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Step 1.1

Move the negative in front of the fraction.

$- \frac{\sqrt{39}}{8} \cdot \frac{- \sqrt{7}}{4} + (\frac{- \sqrt{7}}{4}) (\frac{- \sqrt{39}}{8})$

Step 1.2

Move the negative in front of the fraction.

$- \frac{\sqrt{39}}{8} (- \frac{\sqrt{7}}{4}) + (\frac{- \sqrt{7}}{4}) (\frac{- \sqrt{39}}{8})$

Step 1.3

Multiply $- \frac{\sqrt{39}}{8} (- \frac{\sqrt{7}}{4})$ .

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Step 1.3.1

Multiply $- 1$ by $- 1$ .

$1 \frac{\sqrt{39}}{8} \frac{\sqrt{7}}{4} + (\frac{- \sqrt{7}}{4}) (\frac{- \sqrt{39}}{8})$

Step 1.3.2

Multiply $\frac{\sqrt{39}}{8}$ by $1$ .

$\frac{\sqrt{39}}{8} \cdot \frac{\sqrt{7}}{4} + (\frac{- \sqrt{7}}{4}) (\frac{- \sqrt{39}}{8})$

Step 1.3.3

Multiply $\frac{\sqrt{39}}{8}$ by $\frac{\sqrt{7}}{4}$ .

$\frac{\sqrt{39} \sqrt{7}}{8 \cdot 4} + (\frac{- \sqrt{7}}{4}) (\frac{- \sqrt{39}}{8})$

Step 1.3.4

Combine using the product rule for radicals.

$\frac{\sqrt{39 \cdot 7}}{8 \cdot 4} + (\frac{- \sqrt{7}}{4}) (\frac{- \sqrt{39}}{8})$

Step 1.3.5

Multiply $39$ by $7$ .

$\frac{\sqrt{273}}{8 \cdot 4} + (\frac{- \sqrt{7}}{4}) (\frac{- \sqrt{39}}{8})$

Step 1.3.6

Multiply $8$ by $4$ .

$\frac{\sqrt{273}}{32} + (\frac{- \sqrt{7}}{4}) (\frac{- \sqrt{39}}{8})$

Step 1.4

Move the negative in front of the fraction.

$\frac{\sqrt{273}}{32} - \frac{\sqrt{7}}{4} \cdot \frac{- \sqrt{39}}{8}$

Step 1.5

Move the negative in front of the fraction.

$\frac{\sqrt{273}}{32} - \frac{\sqrt{7}}{4} (- \frac{\sqrt{39}}{8})$

Step 1.6

Multiply $- \frac{\sqrt{7}}{4} (- \frac{\sqrt{39}}{8})$ .

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Step 1.6.1

Multiply $- 1$ by $- 1$ .

$\frac{\sqrt{273}}{32} + 1 \frac{\sqrt{7}}{4} \frac{\sqrt{39}}{8}$

Step 1.6.2

Multiply $\frac{\sqrt{7}}{4}$ by $1$ .

$\frac{\sqrt{273}}{32} + \frac{\sqrt{7}}{4} \cdot \frac{\sqrt{39}}{8}$

Step 1.6.3

Multiply $\frac{\sqrt{7}}{4}$ by $\frac{\sqrt{39}}{8}$ .

$\frac{\sqrt{273}}{32} + \frac{\sqrt{7} \sqrt{39}}{4 \cdot 8}$

Step 1.6.4

Combine using the product rule for radicals.

$\frac{\sqrt{273}}{32} + \frac{\sqrt{7 \cdot 39}}{4 \cdot 8}$

Step 1.6.5

Multiply $7$ by $39$ .

$\frac{\sqrt{273}}{32} + \frac{\sqrt{273}}{4 \cdot 8}$

Step 1.6.6

Multiply $4$ by $8$ .

$\frac{\sqrt{273}}{32} + \frac{\sqrt{273}}{32}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{\sqrt{273} + \sqrt{273}}{32}$

Step 2.2

Add $\sqrt{273}$ and $\sqrt{273}$ .

$\frac{2 \sqrt{273}}{32}$

Step 2.3

Cancel the common factor of $2$ and $32$ .

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Step 2.3.1

Factor $2$ out of $2 \sqrt{273}$ .

$\frac{2 (\sqrt{273})}{32}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $32$ .

$\frac{2 \sqrt{273}}{2 \cdot 16}$

Step 2.3.2.2

Cancel the common factor.

$\frac{2 \sqrt{273}}{2 \cdot 16}$

Step 2.3.2.3

Rewrite the expression.

$\frac{\sqrt{273}}{16}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{273}}{16}$

Decimal Form:

$1.03266947 \dots$