Simplify (5|-2-73|-217)/(22+ square root of 728)

$\frac{5 \cdot | - 2 - 7 \cdot 3 | - 2 \cdot 17}{22 + \sqrt{7 \cdot 28}}$

Simplify the numerator.

Multiply $- 7$ by $3$ .

$\frac{5 \cdot | - 2 - 21 | - 2 \cdot 17}{22 + \sqrt{7 \cdot 28}}$

Subtract $21$ from $- 2$ .

$\frac{5 \cdot | - 23 | - 2 \cdot 17}{22 + \sqrt{7 \cdot 28}}$

The absolute value is the distance between a number and zero. The distance between $- 23$ and $0$ is $23$ .

$\frac{5 \cdot 23 - 2 \cdot 17}{22 + \sqrt{7 \cdot 28}}$

Multiply $5$ by $23$ .

$\frac{115 - 2 \cdot 17}{22 + \sqrt{7 \cdot 28}}$

Multiply $- 2$ by $17$ .

$\frac{115 - 34}{22 + \sqrt{7 \cdot 28}}$

Subtract $34$ from $115$ .

$\frac{81}{22 + \sqrt{7 \cdot 28}}$

Simplify the denominator.

Multiply $7$ by $28$ .

$\frac{81}{22 + \sqrt{196}}$

Rewrite $196$ as $14^{2}$ .

$\frac{81}{22 + \sqrt{14^{2}}}$

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

$\frac{81}{22 + 14}$

Add $22$ and $14$ .

$\frac{81}{36}$

Cancel the common factor of $81$ and $36$ .

Factor $9$ out of $81$ .

$\frac{9 (9)}{36}$

Cancel the common factors.

Factor $9$ out of $36$ .

$\frac{9 \cdot 9}{9 \cdot 4}$

Cancel the common factor.

$\frac{9 \cdot 9}{9 \cdot 4}$

Rewrite the expression.

$\frac{9}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$

Simplify (5*|-2-7*3|-2*17)/(22+ square root of 7*28)