Evaluate (3 square root of 49+(1-5)^2)/((3*4)÷4+3)

$\frac{3 \sqrt{49} + {(1 - 5)}^{2}}{3 \cdot 4 \div 4 + 3}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 \sqrt{49} + {(1 - 5)}^{2}}{3 \cdot 4 \div 4 + 3}$

Divide $3$ by $1$ .

$\frac{3 \sqrt{49} + {(1 - 5)}^{2}}{3 + 3}$

Simplify the numerator.

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

$\frac{3 \sqrt{7^{2}} + {(1 - 5)}^{2}}{3 + 3}$

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

$\frac{3 \cdot 7 + {(1 - 5)}^{2}}{3 + 3}$

Multiply $3$ by $7$ .

$\frac{21 + {(1 - 5)}^{2}}{3 + 3}$

Subtract $5$ from $1$ .

$\frac{21 + {(- 4)}^{2}}{3 + 3}$

Raise $- 4$ to the power of $2$ .

$\frac{21 + 16}{3 + 3}$

Add $21$ and $16$ .

$\frac{37}{3 + 3}$

Add $3$ and $3$ .

$\frac{37}{6}$

The result can be shown in multiple forms.

Exact Form:

$\frac{37}{6}$

Decimal Form:

$6.1\overline{6}$

Mixed Number Form:

$6 \frac{1}{6}$