Solve {l}{sqrt{25*100}}{sqrt{2,25*0,04*1600}}{sqrt{134/9}}

$$\left. \begin{array} { l } { \sqrt { 25 \cdot 100 } } \\ { \sqrt { 2,25 \cdot 0,04 \cdot 1600 } } \\ { \sqrt { 13 \frac { 4 } { 9 } } } \end{array} \right.$$

Sort

$$\frac{11}{3};12;50$$

Solution Steps

Multiply 25 and 100 to get 2500.

$$sort(\sqrt{2500};\sqrt{2,25\times 0,04\times 1600};\sqrt{\frac{13\times 9+4}{9}})$$

Calculate the square root of 2500 and get 50.

$$sort(50;\sqrt{2,25\times 0,04\times 1600};\sqrt{\frac{13\times 9+4}{9}})$$

Multiply 2,25 and 0,04 to get 0,09.

$$sort(50;\sqrt{0,09\times 1600};\sqrt{\frac{13\times 9+4}{9}})$$

Multiply 0,09 and 1600 to get 144.

$$sort(50;\sqrt{144};\sqrt{\frac{13\times 9+4}{9}})$$

Calculate the square root of 144 and get 12.

$$sort(50;12;\sqrt{\frac{13\times 9+4}{9}})$$

Multiply 13 and 9 to get 117.

$$sort(50;12;\sqrt{\frac{117+4}{9}})$$

Add 117 and 4 to get 121.

$$sort(50;12;\sqrt{\frac{121}{9}})$$

Rewrite the square root of the division \frac{121}{9} as the division of square roots \frac{\sqrt{121}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$sort(50;12;\frac{11}{3})$$

Convert decimal numbers in the list 50;12;\frac{11}{3} to fractions.

$$50;12;\frac{11}{3}$$

To sort the list, start from a single element 50.

$$50$$

Insert 12 to the appropriate location in the new list.

$$12;50$$

Insert \frac{11}{3} to the appropriate location in the new list.

$$\frac{11}{3};12;50$$

Evaluate

$$50,\ 12,\ \frac{11}{3}$$