Evaluate square root of 9(3-4)^2+(1-1÷2)^2

$\sqrt{9 {(3 - 4)}^{2}} + {(1 - 1 \div 2)}^{2}$

Step 1

Simplify each term.

Subtract $4$ from $3$ .

$\sqrt{9 {(- 1)}^{2}} + {(1 - 1 \div 2)}^{2}$

Raise $- 1$ to the power of $2$ .

$\sqrt{9 \cdot 1} + {(1 - 1 \div 2)}^{2}$

Multiply $9$ by $1$ .

$\sqrt{9} + {(1 - 1 \div 2)}^{2}$

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

$\sqrt{3^{2}} + {(1 - 1 \div 2)}^{2}$

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

$3 + {(1 - 1 \div 2)}^{2}$

Rewrite the division as a fraction.

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

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $2$ .

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

Apply the product rule to $\frac{1}{2}$ .

$3 + \frac{1^{2}}{2^{2}}$

One to any power is one.

$3 + \frac{1}{2^{2}}$

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

$3 + \frac{1}{4}$

Step 2

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$3 \cdot \frac{4}{4} + \frac{1}{4}$

Step 3

Combine $3$ and $\frac{4}{4}$ .

$\frac{3 \cdot 4}{4} + \frac{1}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 + 1}{4}$

Step 5

Simplify the numerator.

Multiply $3$ by $4$ .

$\frac{12 + 1}{4}$

Add $12$ and $1$ .

$\frac{13}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{4}$

Decimal Form:

$3.25$

Mixed Number Form:

$3 \frac{1}{4}$

Evaluate square root of 9(3-4)^2+(1-1÷2)^2

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