Evaluate ( square root of (92+340)(50-5^2))/3+(492+592-28)/(2^3)+(20*92)/(2^2)+92/2+142

$\frac{\sqrt{(92 + 340) (50 - 5^{2})}}{3} + \frac{4 \cdot 92 + 5 \cdot 92 - 28}{2^{3}} + \frac{20 \cdot 92}{2^{2}} + \frac{92}{2} + 142$

Step 1

Multiply $4$ by $92$ .

$\frac{\sqrt{(92 + 340) (50 - 5^{2})}}{3} + \frac{368 + 5 \cdot 92 - 28}{2^{3}} + \frac{20 \cdot 92}{2^{2}} + \frac{92}{2} + 142$

Step 2

Multiply $5$ by $92$ .

$\frac{\sqrt{(92 + 340) (50 - 5^{2})}}{3} + \frac{368 + 460 - 28}{2^{3}} + \frac{20 \cdot 92}{2^{2}} + \frac{92}{2} + 142$

Step 3

Multiply $20$ by $92$ .

$\frac{\sqrt{(92 + 340) (50 - 5^{2})}}{3} + \frac{368 + 460 - 28}{2^{3}} + \frac{1840}{2^{2}} + \frac{92}{2} + 142$

Step 4

Add $92$ and $340$ .

$\frac{\sqrt{432 (50 - 5^{2})}}{3} + \frac{368 + 460 - 28}{2^{3}} + \frac{1840}{2^{2}} + \frac{92}{2} + 142$

Step 5

Add $368$ and $460$ .

$\frac{\sqrt{432 (50 - 5^{2})}}{3} + \frac{828 - 28}{2^{3}} + \frac{1840}{2^{2}} + \frac{92}{2} + 142$

Step 6

Subtract $28$ from $828$ .

$\frac{\sqrt{432 (50 - 5^{2})}}{3} + \frac{800}{2^{3}} + \frac{1840}{2^{2}} + \frac{92}{2} + 142$

Step 7

Find the common denominator.

Raise $2$ to the power of $3$ .

$\frac{\sqrt{432 (50 - 5^{2})}}{3} + \frac{800}{8} + \frac{1840}{2^{2}} + \frac{92}{2} + 142$

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

$\frac{\sqrt{432 (50 - 5^{2})}}{3} + \frac{800}{8} + \frac{1840}{4} + \frac{92}{2} + 142$

Multiply $\frac{\sqrt{432 (50 - 5^{2})}}{3}$ by $\frac{8}{8}$ .

$\frac{\sqrt{432 (50 - 5^{2})}}{3} \cdot \frac{8}{8} + \frac{800}{8} + \frac{1840}{4} + \frac{92}{2} + 142$

Multiply $\frac{\sqrt{432 (50 - 5^{2})}}{3}$ by $\frac{8}{8}$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{3 \cdot 8} + \frac{800}{8} + \frac{1840}{4} + \frac{92}{2} + 142$

Multiply $\frac{800}{8}$ by $\frac{3}{3}$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{3 \cdot 8} + \frac{800}{8} \cdot \frac{3}{3} + \frac{1840}{4} + \frac{92}{2} + 142$

Multiply $\frac{800}{8}$ by $\frac{3}{3}$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{3 \cdot 8} + \frac{800 \cdot 3}{8 \cdot 3} + \frac{1840}{4} + \frac{92}{2} + 142$

Multiply $\frac{1840}{4}$ by $\frac{6}{6}$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{3 \cdot 8} + \frac{800 \cdot 3}{8 \cdot 3} + \frac{1840}{4} \cdot \frac{6}{6} + \frac{92}{2} + 142$

Multiply $\frac{1840}{4}$ by $\frac{6}{6}$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{3 \cdot 8} + \frac{800 \cdot 3}{8 \cdot 3} + \frac{1840 \cdot 6}{4 \cdot 6} + \frac{92}{2} + 142$

Multiply $\frac{92}{2}$ by $\frac{12}{12}$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{3 \cdot 8} + \frac{800 \cdot 3}{8 \cdot 3} + \frac{1840 \cdot 6}{4 \cdot 6} + \frac{92}{2} \cdot \frac{12}{12} + 142$

Multiply $\frac{92}{2}$ by $\frac{12}{12}$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{3 \cdot 8} + \frac{800 \cdot 3}{8 \cdot 3} + \frac{1840 \cdot 6}{4 \cdot 6} + \frac{92 \cdot 12}{2 \cdot 12} + 142$

Write $142$ as a fraction with denominator $1$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{3 \cdot 8} + \frac{800 \cdot 3}{8 \cdot 3} + \frac{1840 \cdot 6}{4 \cdot 6} + \frac{92 \cdot 12}{2 \cdot 12} + \frac{142}{1}$

Multiply $\frac{142}{1}$ by $\frac{24}{24}$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{3 \cdot 8} + \frac{800 \cdot 3}{8 \cdot 3} + \frac{1840 \cdot 6}{4 \cdot 6} + \frac{92 \cdot 12}{2 \cdot 12} + \frac{142}{1} \cdot \frac{24}{24}$

Multiply $\frac{142}{1}$ by $\frac{24}{24}$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{3 \cdot 8} + \frac{800 \cdot 3}{8 \cdot 3} + \frac{1840 \cdot 6}{4 \cdot 6} + \frac{92 \cdot 12}{2 \cdot 12} + \frac{142 \cdot 24}{24}$

Multiply $3$ by $8$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{24} + \frac{800 \cdot 3}{8 \cdot 3} + \frac{1840 \cdot 6}{4 \cdot 6} + \frac{92 \cdot 12}{2 \cdot 12} + \frac{142 \cdot 24}{24}$

Reorder the factors of $8 \cdot 3$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{24} + \frac{800 \cdot 3}{3 \cdot 8} + \frac{1840 \cdot 6}{4 \cdot 6} + \frac{92 \cdot 12}{2 \cdot 12} + \frac{142 \cdot 24}{24}$

Multiply $3$ by $8$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{24} + \frac{800 \cdot 3}{24} + \frac{1840 \cdot 6}{4 \cdot 6} + \frac{92 \cdot 12}{2 \cdot 12} + \frac{142 \cdot 24}{24}$

Multiply $4$ by $6$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{24} + \frac{800 \cdot 3}{24} + \frac{1840 \cdot 6}{24} + \frac{92 \cdot 12}{2 \cdot 12} + \frac{142 \cdot 24}{24}$

Multiply $2$ by $12$ .

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8}{24} + \frac{800 \cdot 3}{24} + \frac{1840 \cdot 6}{24} + \frac{92 \cdot 12}{24} + \frac{142 \cdot 24}{24}$

Step 8

Combine the numerators over the common denominator.

$\frac{\sqrt{432 (50 - 5^{2})} \cdot 8 + 800 \cdot 3 + 1840 \cdot 6 + 92 \cdot 12 + 142 \cdot 24}{24}$

Step 9

Simplify each term.

Raise $5$ to the power of $2$ .

$\frac{\sqrt{432 (50 - 1 \cdot 25)} \cdot 8 + 800 \cdot 3 + 1840 \cdot 6 + 92 \cdot 12 + 142 \cdot 24}{24}$

Multiply $- 1$ by $25$ .

$\frac{\sqrt{432 (50 - 25)} \cdot 8 + 800 \cdot 3 + 1840 \cdot 6 + 92 \cdot 12 + 142 \cdot 24}{24}$

Subtract $25$ from $50$ .

$\frac{\sqrt{432 \cdot 25} \cdot 8 + 800 \cdot 3 + 1840 \cdot 6 + 92 \cdot 12 + 142 \cdot 24}{24}$

Multiply $432$ by $25$ .

$\frac{\sqrt{10800} \cdot 8 + 800 \cdot 3 + 1840 \cdot 6 + 92 \cdot 12 + 142 \cdot 24}{24}$

Rewrite $10800$ as $60^{2} \cdot 3$ .

Factor $3600$ out of $10800$ .

$\frac{\sqrt{3600 (3)} \cdot 8 + 800 \cdot 3 + 1840 \cdot 6 + 92 \cdot 12 + 142 \cdot 24}{24}$

Rewrite $3600$ as $60^{2}$ .

$\frac{\sqrt{60^{2} \cdot 3} \cdot 8 + 800 \cdot 3 + 1840 \cdot 6 + 92 \cdot 12 + 142 \cdot 24}{24}$

Pull terms out from under the radical.

$\frac{60 \sqrt{3} \cdot 8 + 800 \cdot 3 + 1840 \cdot 6 + 92 \cdot 12 + 142 \cdot 24}{24}$

Multiply $8$ by $60$ .

$\frac{480 \sqrt{3} + 800 \cdot 3 + 1840 \cdot 6 + 92 \cdot 12 + 142 \cdot 24}{24}$

Multiply $800$ by $3$ .

$\frac{480 \sqrt{3} + 2400 + 1840 \cdot 6 + 92 \cdot 12 + 142 \cdot 24}{24}$

Multiply $1840$ by $6$ .

$\frac{480 \sqrt{3} + 2400 + 11040 + 92 \cdot 12 + 142 \cdot 24}{24}$

Multiply $92$ by $12$ .

$\frac{480 \sqrt{3} + 2400 + 11040 + 1104 + 142 \cdot 24}{24}$

Multiply $142$ by $24$ .

$\frac{480 \sqrt{3} + 2400 + 11040 + 1104 + 3408}{24}$

Step 10

Reduce the expression by cancelling the common factors.

Add $2400$ and $11040$ .

$\frac{480 \sqrt{3} + 13440 + 1104 + 3408}{24}$

Simplify by adding numbers.

Add $13440$ and $1104$ .

$\frac{480 \sqrt{3} + 14544 + 3408}{24}$

Add $14544$ and $3408$ .

$\frac{480 \sqrt{3} + 17952}{24}$

Cancel the common factor of $480 \sqrt{3} + 17952$ and $24$ .

Factor $24$ out of $480 \sqrt{3}$ .

$\frac{24 (20 \sqrt{3}) + 17952}{24}$

Factor $24$ out of $17952$ .

$\frac{24 (20 \sqrt{3}) + 24 \cdot 748}{24}$

Factor $24$ out of $24 (20 \sqrt{3}) + 24 (748)$ .

$\frac{24 (20 \sqrt{3} + 748)}{24}$

Cancel the common factors.

Factor $24$ out of $24$ .

$\frac{24 (20 \sqrt{3} + 748)}{24 (1)}$

Cancel the common factor.

$\frac{24 (20 \sqrt{3} + 748)}{24 \cdot 1}$

Rewrite the expression.

$\frac{20 \sqrt{3} + 748}{1}$

Divide $20 \sqrt{3} + 748$ by $1$ .

$20 \sqrt{3} + 748$

Step 11

The result can be shown in multiple forms.

Exact Form:

$20 \sqrt{3} + 748$

Decimal Form:

$782.64101615 \dots$

Evaluate ( square root of (92+340)(50-5^2))/3+(4*92+5*92-28)/(2^3)+(20*92)/(2^2)+92/2+142

Related Questions

Evaluate ( square root of (92+340)(50-5^2))/3+(492+592-28)/(2^3)+(20*92)/(2^2)+92/2+142