Solve (48*25.6+19*18.6+4*16.6+7*15.6+29*9.6+12*8.6+15*7.6+6.6*11+23*0.6+8.4*12)div(48^2+19^2+4^2+7^2+{29}^{2}+{12}^{2}+{15}^2+{11}^2+{23}^2+{12}^2)

$$(48 \times 25.6+19 \times 18.6+4 \times 16.6+7 \times 15.6+29 \times 9.6+12 \times 8.6+15 \times 7.6+6.6 \times 11+23 \times 0.6+8.4 \times 12) \div ( { 48 }^{ 2 } + { 19 }^{ 2 } + { 4 }^{ 2 } + { 7 }^{ 2 } + { 29 }^{ 2 } + { 12 }^{ 2 } + { 15 }^{ 2 } + { 11 }^{ 2 } + { 23 }^{ 2 } + { 12 }^{ 2 } )$$

Evaluate

$$\frac{12203}{23670}\approx 0.515547106$$

Solution Steps

Multiply 48 and 25.6 to get 1228.8.

$$\frac{1228.8+19\times 18.6+4\times 16.6+7\times 15.6+29\times 9.6+12\times 8.6+15\times 7.6+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Multiply 19 and 18.6 to get 353.4.

$$\frac{1228.8+353.4+4\times 16.6+7\times 15.6+29\times 9.6+12\times 8.6+15\times 7.6+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 1228.8 and 353.4 to get 1582.2.

$$\frac{1582.2+4\times 16.6+7\times 15.6+29\times 9.6+12\times 8.6+15\times 7.6+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Multiply 4 and 16.6 to get 66.4.

$$\frac{1582.2+66.4+7\times 15.6+29\times 9.6+12\times 8.6+15\times 7.6+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 1582.2 and 66.4 to get 1648.6.

$$\frac{1648.6+7\times 15.6+29\times 9.6+12\times 8.6+15\times 7.6+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Multiply 7 and 15.6 to get 109.2.

$$\frac{1648.6+109.2+29\times 9.6+12\times 8.6+15\times 7.6+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 1648.6 and 109.2 to get 1757.8.

$$\frac{1757.8+29\times 9.6+12\times 8.6+15\times 7.6+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Multiply 29 and 9.6 to get 278.4.

$$\frac{1757.8+278.4+12\times 8.6+15\times 7.6+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 1757.8 and 278.4 to get 2036.2.

$$\frac{2036.2+12\times 8.6+15\times 7.6+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Multiply 12 and 8.6 to get 103.2.

$$\frac{2036.2+103.2+15\times 7.6+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 2036.2 and 103.2 to get 2139.4.

$$\frac{2139.4+15\times 7.6+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Multiply 15 and 7.6 to get 114.

$$\frac{2139.4+114+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 2139.4 and 114 to get 2253.4.

$$\frac{2253.4+6.6\times 11+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Multiply 6.6 and 11 to get 72.6.

$$\frac{2253.4+72.6+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 2253.4 and 72.6 to get 2326.

$$\frac{2326+23\times 0.6+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Multiply 23 and 0.6 to get 13.8.

$$\frac{2326+13.8+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 2326 and 13.8 to get 2339.8.

$$\frac{2339.8+8.4\times 12}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Multiply 8.4 and 12 to get 100.8.

$$\frac{2339.8+100.8}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 2339.8 and 100.8 to get 2440.6.

$$\frac{2440.6}{48^{2}+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Calculate 48 to the power of 2 and get 2304.

$$\frac{2440.6}{2304+19^{2}+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Calculate 19 to the power of 2 and get 361.

$$\frac{2440.6}{2304+361+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 2304 and 361 to get 2665.

$$\frac{2440.6}{2665+4^{2}+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{2440.6}{2665+16+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 2665 and 16 to get 2681.

$$\frac{2440.6}{2681+7^{2}+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{2440.6}{2681+49+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 2681 and 49 to get 2730.

$$\frac{2440.6}{2730+29^{2}+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Calculate 29 to the power of 2 and get 841.

$$\frac{2440.6}{2730+841+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 2730 and 841 to get 3571.

$$\frac{2440.6}{3571+12^{2}+15^{2}+11^{2}+23^{2}+12^{2}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{2440.6}{3571+144+15^{2}+11^{2}+23^{2}+12^{2}}$$

Add 3571 and 144 to get 3715.

$$\frac{2440.6}{3715+15^{2}+11^{2}+23^{2}+12^{2}}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{2440.6}{3715+225+11^{2}+23^{2}+12^{2}}$$

Add 3715 and 225 to get 3940.

$$\frac{2440.6}{3940+11^{2}+23^{2}+12^{2}}$$

Calculate 11 to the power of 2 and get 121.

$$\frac{2440.6}{3940+121+23^{2}+12^{2}}$$

Add 3940 and 121 to get 4061.

$$\frac{2440.6}{4061+23^{2}+12^{2}}$$

Calculate 23 to the power of 2 and get 529.

$$\frac{2440.6}{4061+529+12^{2}}$$

Add 4061 and 529 to get 4590.

$$\frac{2440.6}{4590+12^{2}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{2440.6}{4590+144}$$

Add 4590 and 144 to get 4734.

$$\frac{2440.6}{4734}$$

Expand \frac{2440.6}{4734} by multiplying both numerator and the denominator by 10.

$$\frac{24406}{47340}$$

Reduce the fraction \frac{24406}{47340} to lowest terms by extracting and canceling out 2.

$$\frac{12203}{23670}$$

Factor

$$\frac{12203}{2 \cdot 5 \cdot 263 \cdot 3 ^ {2}} = 0.5155471060414026$$