Question

How do we simplify the square root of 8 – the square root of 66?

Answer 1

Hint:To solve this question, first we will simplify the square root of 8 and then simplify the square root of 66. Then, we will find the difference of the simplified form of the square root of both of the numbers.

Complete step by step solution:
First we will simplify the square root of each of the given numbers separately.
Now, Simplify the square root of 8 :
8 can be factored to 8 $ = 4.2$So,
 $\sqrt 8 = \sqrt {4.2} = \sqrt 4 .\sqrt 2 = 2\sqrt 2 $
Hence, $2\sqrt 2 $ is the simplification of 8.
Again,
Simplify the square root of 66 :
$
  \sqrt {66} = \sqrt {33.2} \\
  \,\,\,\,\,\,\,\,\,\,\, = \sqrt {33} \sqrt 2 \\
 $
Now,
$
  \therefore \sqrt 8 - \sqrt {66} \\
   = 2\sqrt 2 - \sqrt {33} .\sqrt 2 \\
$
Take $\sqrt 2 $ as a common:
$ = \sqrt 2 (2 - \sqrt {33} )$
Or, according to the Square Root rule:
$b\sqrt a - c\sqrt a = (b - c)\sqrt a $
or $2\sqrt 2 - \sqrt {33} \sqrt 2 = (2 - \sqrt {33} )\sqrt 2 $
Hence, the square root of 8 – the square root of 66 is $\sqrt 2 (2 - \sqrt {33} )$ .

Note:- When utilizing math root rules, first note that we can't have a negative number under a square root or some other much number root — in any event, not in essential analytics. On the off chance that you have a much number root, you need the total worth bars on the appropriate response since, regardless of whether an is positive or negative, the appropriate response is positive. In the event that it's an odd number root, you needn't bother with the supreme worth bars.