Algebra Examples

$\sqrt{15} \cdot \sqrt{\frac{35}{12}}$

Step 1

Combine using the product rule for radicals.

$\sqrt{15 \cdot \frac{35}{12}}$

Step 2

Combine $15$ and $\frac{35}{12}$ .

$\sqrt{\frac{15 \cdot 35}{12}}$

Step 3

Reduce the expression $\frac{15 \cdot 35}{12}$ by cancelling the common factors.

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Step 3.1

Factor $3$ out of $15 \cdot 35$ .

$\sqrt{\frac{3 (5 \cdot 35)}{12}}$

Step 3.2

Factor $3$ out of $12$ .

$\sqrt{\frac{3 (5 \cdot 35)}{3 (4)}}$

Step 3.3

Cancel the common factor.

$\sqrt{\frac{3 (5 \cdot 35)}{3 \cdot 4}}$

Step 3.4

Rewrite the expression.

$\sqrt{\frac{5 \cdot 35}{4}}$

Step 4

Multiply $5$ by $35$ .

$\sqrt{\frac{175}{4}}$

Step 5

Rewrite $\sqrt{\frac{175}{4}}$ as $\frac{\sqrt{175}}{\sqrt{4}}$ .

$\frac{\sqrt{175}}{\sqrt{4}}$

Step 6

Simplify the numerator.

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Step 6.1

Rewrite $175$ as $5^{2} \cdot 7$ .

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Step 6.1.1

Factor $25$ out of $175$ .

$\frac{\sqrt{25 (7)}}{\sqrt{4}}$

Step 6.1.2

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

$\frac{\sqrt{5^{2} \cdot 7}}{\sqrt{4}}$

Step 6.2

Pull terms out from under the radical.

$\frac{5 \sqrt{7}}{\sqrt{4}}$

Step 7

Simplify the denominator.

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Step 7.1

Rewrite $4$ as $2^{2}$ .

$\frac{5 \sqrt{7}}{\sqrt{2^{2}}}$

Step 7.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{5 \sqrt{7}}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{7}}{2}$

Decimal Form:

$6.61437827 \dots$