Simplify (2 1/3+2 2/3)*(198 square root of 18)

$(2 \frac{1}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Step 1

Convert

$2 \frac{1}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$(2 + \frac{1}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Add

$2$ and

$\frac{1}{3}$ .

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$(2 \cdot \frac{3}{3} + \frac{1}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Combine

$2$ and

$\frac{3}{3}$ .

$(\frac{2 \cdot 3}{3} + \frac{1}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Combine the numerators over the common denominator.

$(\frac{2 \cdot 3 + 1}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Simplify the numerator.

Multiply

$2$ by

$3$ .

$(\frac{6 + 1}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Add

$6$ and

$1$ .

$(\frac{7}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Step 2

Convert

$2 \frac{2}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$(\frac{7}{3} + 2 + \frac{2}{3}) \cdot (198 \sqrt{18})$

Add

$2$ and

$\frac{2}{3}$ .

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$(\frac{7}{3} + 2 \cdot \frac{3}{3} + \frac{2}{3}) \cdot (198 \sqrt{18})$

Combine

$2$ and

$\frac{3}{3}$ .

$(\frac{7}{3} + \frac{2 \cdot 3}{3} + \frac{2}{3}) \cdot (198 \sqrt{18})$

Combine the numerators over the common denominator.

$(\frac{7}{3} + \frac{2 \cdot 3 + 2}{3}) \cdot (198 \sqrt{18})$

Simplify the numerator.

Multiply

$2$ by

$3$ .

$(\frac{7}{3} + \frac{6 + 2}{3}) \cdot (198 \sqrt{18})$

Add

$6$ and

$2$ .

$(\frac{7}{3} + \frac{8}{3}) \cdot (198 \sqrt{18})$

Step 3

Combine the numerators over the common denominator.

$\frac{7 + 8}{3} \cdot (198 \sqrt{18})$

Step 4

Add

$7$ and

$8$ .

$\frac{15}{3} \cdot (198 \sqrt{18})$

Step 5

Cancel the common factor of

$3$ .

Factor

$3$ out of

$198 \sqrt{18}$ .

$\frac{15}{3} \cdot (3 (66 \sqrt{18}))$

Cancel the common factor.

$\frac{15}{3} \cdot (3 (66 \sqrt{18}))$

Rewrite the expression.

$15 \cdot (66 \sqrt{18})$

Step 6

Multiply

$66$ by

$15$ .

$990 \cdot \sqrt{18}$

Step 7

Rewrite

$18$ as

$3^{2} \cdot 2$ .

Factor

$9$ out of

$18$ .

$990 \cdot \sqrt{9 (2)}$

Rewrite

$9$ as

$3^{2}$ .

$990 \cdot \sqrt{3^{2} \cdot 2}$

Step 8

Pull terms out from under the radical.

$990 \cdot (3 \sqrt{2})$

Step 9

Multiply

$3$ by

$990$ .

$2970 \sqrt{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$2970 \sqrt{2}$

Decimal Form:

$4200.21428024 \dots$

Simplify (2 1/3+2 2/3)*(198 square root of 18)

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