Answer:
Sometimes it's better to leave them as roots because it's easier sometimes to solve problems with them still as roots
Answer:
We choose to leave radicals as roots without calculating them because calculating the square roots of a non perfect squares result in an irrational, non terminating decimal.
Step-by-step explanation:
Why do we do Radicals in the first place?
Radicals are used to write the square root or the nth root of a number. We sometimes leave specific numbers (non-perfect squares) as a radical because the output would be infinity
Example:
[tex]\sqrt45[/tex] is not a perfect square, it lies between [tex]\sqrt36[/tex] and [tex]\sqrt49[/tex]
This means the number lies in between 6 and 7
The true root of 45 is irrational. Recall that irrational numbers are numbers of non-perfect squares. [tex]\sqrt45[/tex] = 6.7082039.......
Simplify:
[tex]\sqrt 45 = \sqrt 9 * \sqrt 5\\[/tex]
[tex]= \sqrt3^2 * \sqrt 5\\\\ \\= 3\sqrt5[/tex]
We choose not to pursue simplifying this because [tex]\sqrt5[/tex] is irrational (square root of a non-perfect square)
Summary:
We choose to leave radicals as roots without calculating them because calculating the square roots of a non perfect squares result in an irrational, non terminating decimal.
-Chetan K
