Question

Write in descending order\[\ 7\sqrt{3}\] and \[3\sqrt{7}\]

Answer 1

Hint: In this question, we need to arrange the given numbers in descending order. First we need to rewrite the given terms in proper square root and then compare them . Then arrange them in descending order. Descending order is the process of arranging the given numbers from larger value to smaller value .

Complete answer:
Given, \[7\sqrt{3}\] and \[3\sqrt{7}\]
Now we need to rewrite both the given numbers in proper square root.
Now,
\[7\sqrt{3} = \sqrt{7 \times 7 \times 3}\]
By multiplying,
We get,
\[7\sqrt{3} = \sqrt{147}\]
Then,
\[3\sqrt{7} = \sqrt{3 \times 3 \times 7}\]
By multiplying,
We get,
\[3\sqrt{7} = \sqrt{61}\]
Now we need to compare both the numbers in square root .
Thus \[\sqrt{147}\] is greater than \[\sqrt{61}\]
Then we need to arrange in descending order.
⇒ \[\sqrt{147} > \sqrt{61}\]
Thus ,
\[7\sqrt{3} > 3\sqrt{7}\]
Final answer :
The descending order of \[7\sqrt{3}\] and \[3\sqrt{7}\] is \[7\sqrt{3} > 3\sqrt{7}\]

Additional information :
The symbol of descending order is greater than the symbol that is \[>\] whereas for ascending order is less than the symbol that is \[<\] . A simple example for descending order is \[10 > 9 > 8 > 7\] also for ascending order is \[10 < 9 < 8 < 7\] . Numbers like whole numbers, natural numbers, fractions, integers, etc…can be arranged in descending order.

Note:
The concept used in this question is arranging the real numbers in descending order. First, We should see the question properly whether it is ascending order or descending order. The opposite of descending order is ascending order. Whereas ascending order is the process of arranging the given numbers from smaller value to larger value .