Solve {l}{sqrt6^2*2^8}{sqrt{20}*sqrt{5}-frac{sqrt{63}}{sqrt{7}}}

$$\left. \begin{array} { l } { \sqrt { 6 } ^ { 2 } \cdot 2 ^ { 8 } } \\ { \sqrt { 20 } \cdot \sqrt { 5 } - \frac { \sqrt { 63 } } { \sqrt { 7 } } } \end{array} \right.$$

Sort

$$7,1536$$

Solution Steps

The square of \sqrt{6} is 6.

$$sort(6\times 2^{8},\sqrt{20}\sqrt{5}-\frac{\sqrt{63}}{\sqrt{7}})$$

Calculate 2 to the power of 8 and get 256.

$$sort(6\times 256,\sqrt{20}\sqrt{5}-\frac{\sqrt{63}}{\sqrt{7}})$$

Multiply 6 and 256 to get 1536.

$$sort(1536,\sqrt{20}\sqrt{5}-\frac{\sqrt{63}}{\sqrt{7}})$$

Factor 20=5\times 4. Rewrite the square root of the product \sqrt{5\times 4} as the product of square roots \sqrt{5}\sqrt{4}.

$$sort(1536,\sqrt{5}\sqrt{4}\sqrt{5}-\frac{\sqrt{63}}{\sqrt{7}})$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$sort(1536,5\sqrt{4}-\frac{\sqrt{63}}{\sqrt{7}})$$

Calculate the square root of 4 and get 2.

$$sort(1536,5\times 2-\frac{\sqrt{63}}{\sqrt{7}})$$

Multiply 5 and 2 to get 10.

$$sort(1536,10-\frac{\sqrt{63}}{\sqrt{7}})$$

Rewrite the division of square roots \frac{\sqrt{63}}{\sqrt{7}} as the square root of the division \sqrt{\frac{63}{7}} and perform the division.

$$sort(1536,10-\sqrt{9})$$

Calculate the square root of 9 and get 3.

$$sort(1536,10-3)$$

Subtract 3 from 10 to get 7.

$$sort(1536,7)$$

To sort the list, start from a single element 1536.

$$1536$$

Insert 7 to the appropriate location in the new list.

$$7,1536$$

Evaluate

$$1536,\ 7$$