Algebra Examples

$3 \sqrt{\frac{7}{25}} - \sqrt{\frac{28}{25}} + \sqrt{\frac{63}{25}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\sqrt{\frac{7}{25}}$ as $\frac{\sqrt{7}}{\sqrt{25}}$ .

$3 \frac{\sqrt{7}}{\sqrt{25}} - \sqrt{\frac{28}{25}} + \sqrt{\frac{63}{25}}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

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

$3 \frac{\sqrt{7}}{\sqrt{5^{2}}} - \sqrt{\frac{28}{25}} + \sqrt{\frac{63}{25}}$

Step 1.2.2

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

$3 \frac{\sqrt{7}}{5} - \sqrt{\frac{28}{25}} + \sqrt{\frac{63}{25}}$

Step 1.3

Combine $3$ and $\frac{\sqrt{7}}{5}$ .

$\frac{3 \sqrt{7}}{5} - \sqrt{\frac{28}{25}} + \sqrt{\frac{63}{25}}$

Step 1.4

Rewrite $\sqrt{\frac{28}{25}}$ as $\frac{\sqrt{28}}{\sqrt{25}}$ .

$\frac{3 \sqrt{7}}{5} - \frac{\sqrt{28}}{\sqrt{25}} + \sqrt{\frac{63}{25}}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 1.5.1.1

Factor $4$ out of $28$ .

$\frac{3 \sqrt{7}}{5} - \frac{\sqrt{4 (7)}}{\sqrt{25}} + \sqrt{\frac{63}{25}}$

Step 1.5.1.2

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

$\frac{3 \sqrt{7}}{5} - \frac{\sqrt{2^{2} \cdot 7}}{\sqrt{25}} + \sqrt{\frac{63}{25}}$

Step 1.5.2

Pull terms out from under the radical.

$\frac{3 \sqrt{7}}{5} - \frac{2 \sqrt{7}}{\sqrt{25}} + \sqrt{\frac{63}{25}}$

Step 1.6

Simplify the denominator.

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Step 1.6.1

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

$\frac{3 \sqrt{7}}{5} - \frac{2 \sqrt{7}}{\sqrt{5^{2}}} + \sqrt{\frac{63}{25}}$

Step 1.6.2

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

$\frac{3 \sqrt{7}}{5} - \frac{2 \sqrt{7}}{5} + \sqrt{\frac{63}{25}}$

Step 1.7

Rewrite $\sqrt{\frac{63}{25}}$ as $\frac{\sqrt{63}}{\sqrt{25}}$ .

$\frac{3 \sqrt{7}}{5} - \frac{2 \sqrt{7}}{5} + \frac{\sqrt{63}}{\sqrt{25}}$

Step 1.8

Simplify the numerator.

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Step 1.8.1

Rewrite $63$ as $3^{2} \cdot 7$ .

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Step 1.8.1.1

Factor $9$ out of $63$ .

$\frac{3 \sqrt{7}}{5} - \frac{2 \sqrt{7}}{5} + \frac{\sqrt{9 (7)}}{\sqrt{25}}$

Step 1.8.1.2

Rewrite $9$ as $3^{2}$ .

$\frac{3 \sqrt{7}}{5} - \frac{2 \sqrt{7}}{5} + \frac{\sqrt{3^{2} \cdot 7}}{\sqrt{25}}$

Step 1.8.2

Pull terms out from under the radical.

$\frac{3 \sqrt{7}}{5} - \frac{2 \sqrt{7}}{5} + \frac{3 \sqrt{7}}{\sqrt{25}}$

Step 1.9

Simplify the denominator.

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Step 1.9.1

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

$\frac{3 \sqrt{7}}{5} - \frac{2 \sqrt{7}}{5} + \frac{3 \sqrt{7}}{\sqrt{5^{2}}}$

Step 1.9.2

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

$\frac{3 \sqrt{7}}{5} - \frac{2 \sqrt{7}}{5} + \frac{3 \sqrt{7}}{5}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{3 \sqrt{7} - 2 \sqrt{7} + 3 \sqrt{7}}{5}$

Step 2.2

Subtract $2 \sqrt{7}$ from $3 \sqrt{7}$ .

$\frac{\sqrt{7} + 3 \sqrt{7}}{5}$

Step 2.3

Add $\sqrt{7}$ and $3 \sqrt{7}$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$2.11660104 \dots$