Evaluate square root of 48/147

$\sqrt{\frac{48}{147}}$

Step 1

Cancel the common factor of $48$ and $147$ .

Factor $3$ out of $48$ .

$\sqrt{\frac{3 (16)}{147}}$

Cancel the common factors.

Factor $3$ out of $147$ .

$\sqrt{\frac{3 \cdot 16}{3 \cdot 49}}$

Cancel the common factor.

$\sqrt{\frac{3 \cdot 16}{3 \cdot 49}}$

Rewrite the expression.

$\sqrt{\frac{16}{49}}$

Step 2

Rewrite $\sqrt{\frac{16}{49}}$ as $\frac{\sqrt{16}}{\sqrt{49}}$ .

$\frac{\sqrt{16}}{\sqrt{49}}$

Step 3

Simplify the numerator.

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2}}}{\sqrt{49}}$

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

$\frac{4}{\sqrt{49}}$

Step 4

Simplify the denominator.

Rewrite $49$ as $7^{2}$ .

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

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

$\frac{4}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{7}$

Decimal Form:

$0.\overline{571428}$