Basic Math Examples

$\frac{6 - 7 \sqrt{10}}{4 + \sqrt{15}} \cdot \frac{4 - \sqrt{15}}{4 - \sqrt{15}}$

Step 1

Cancel the common factor of $4 - \sqrt{15}$ .

Tap for more steps...

Step 1.1

Cancel the common factor.

$\frac{6 - 7 \sqrt{10}}{4 + \sqrt{15}} \cdot \frac{4 - \sqrt{15}}{4 - \sqrt{15}}$

Step 1.2

Rewrite the expression.

$\frac{6 - 7 \sqrt{10}}{4 + \sqrt{15}} \cdot 1$

Step 2

Multiply $\frac{6 - 7 \sqrt{10}}{4 + \sqrt{15}}$ by $1$ .

$\frac{6 - 7 \sqrt{10}}{4 + \sqrt{15}}$

Step 3

Multiply $\frac{6 - 7 \sqrt{10}}{4 + \sqrt{15}}$ by $\frac{4 - \sqrt{15}}{4 - \sqrt{15}}$ .

$\frac{6 - 7 \sqrt{10}}{4 + \sqrt{15}} \cdot \frac{4 - \sqrt{15}}{4 - \sqrt{15}}$

Step 4

Combine fractions.

Tap for more steps...

Step 4.1

Multiply $\frac{6 - 7 \sqrt{10}}{4 + \sqrt{15}}$ by $\frac{4 - \sqrt{15}}{4 - \sqrt{15}}$ .

$\frac{(6 - 7 \sqrt{10}) (4 - \sqrt{15})}{(4 + \sqrt{15}) (4 - \sqrt{15})}$

Step 4.2

Expand the denominator using the FOIL method.

$\frac{(6 - 7 \sqrt{10}) (4 - \sqrt{15})}{16 - 4 \sqrt{15} + \sqrt{15} \cdot 4 - {\sqrt{15}}^{2}}$

Step 4.3

Simplify.

$\frac{(6 - 7 \sqrt{10}) (4 - \sqrt{15})}{1}$

Step 4.4

Divide $(6 - 7 \sqrt{10}) (4 - \sqrt{15})$ by $1$ .

$(6 - 7 \sqrt{10}) (4 - \sqrt{15})$

Step 5

Expand $(6 - 7 \sqrt{10}) (4 - \sqrt{15})$ using the FOIL Method.

Tap for more steps...

Step 5.1

Apply the distributive property.

$6 (4 - \sqrt{15}) - 7 \sqrt{10} (4 - \sqrt{15})$

Step 5.2

Apply the distributive property.

$6 \cdot 4 + 6 (- \sqrt{15}) - 7 \sqrt{10} (4 - \sqrt{15})$

Step 5.3

Apply the distributive property.

$6 \cdot 4 + 6 (- \sqrt{15}) - 7 \sqrt{10} \cdot 4 - 7 \sqrt{10} (- \sqrt{15})$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

Multiply $6$ by $4$ .

$24 + 6 (- \sqrt{15}) - 7 \sqrt{10} \cdot 4 - 7 \sqrt{10} (- \sqrt{15})$

Step 6.2

Multiply $- 1$ by $6$ .

$24 - 6 \sqrt{15} - 7 \sqrt{10} \cdot 4 - 7 \sqrt{10} (- \sqrt{15})$

Step 6.3

Multiply $4$ by $- 7$ .

$24 - 6 \sqrt{15} - 28 \sqrt{10} - 7 \sqrt{10} (- \sqrt{15})$

Step 6.4

Multiply $- 7 \sqrt{10} (- \sqrt{15})$ .

Tap for more steps...

Step 6.4.1

Multiply $- 1$ by $- 7$ .

$24 - 6 \sqrt{15} - 28 \sqrt{10} + 7 \sqrt{10} \sqrt{15}$

Step 6.4.2

Combine using the product rule for radicals.

$24 - 6 \sqrt{15} - 28 \sqrt{10} + 7 \sqrt{15 \cdot 10}$

Step 6.4.3

Multiply $15$ by $10$ .

$24 - 6 \sqrt{15} - 28 \sqrt{10} + 7 \sqrt{150}$

Step 6.5

Rewrite $150$ as $5^{2} \cdot 6$ .

Tap for more steps...

Step 6.5.1

Factor $25$ out of $150$ .

$24 - 6 \sqrt{15} - 28 \sqrt{10} + 7 \sqrt{25 (6)}$

Step 6.5.2

Rewrite $25$ as $5^{2}$ .

$24 - 6 \sqrt{15} - 28 \sqrt{10} + 7 \sqrt{5^{2} \cdot 6}$

Step 6.6

Pull terms out from under the radical.

$24 - 6 \sqrt{15} - 28 \sqrt{10} + 7 (5 \sqrt{6})$

Step 6.7

Multiply $5$ by $7$ .

$24 - 6 \sqrt{15} - 28 \sqrt{10} + 35 \sqrt{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$24 - 6 \sqrt{15} - 28 \sqrt{10} + 35 \sqrt{6}$

Decimal Form:

$- 2.04953356 \dots$