Simplify 3 square root of 7/25- square root of 28/25+ square root of 63/25

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

Simplify each term.

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

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

Simplify the denominator.

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

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

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

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

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

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

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

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

Simplify the numerator.

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

Factor $4$ out of $28$ .

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

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

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

Pull terms out from under the radical.

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

Simplify the denominator.

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

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

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

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

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

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

Simplify the numerator.

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

Factor $9$ out of $63$ .

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

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

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

Pull terms out from under the radical.

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

Simplify the denominator.

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

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

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

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

Simplify terms.

Combine the numerators over the common denominator.

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

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

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

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$2.11660104 \dots$

Simplify 3 square root of 7/25- square root of 28/25+ square root of 63/25

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