Answer:
[tex]2\sqrt{17}[/tex]
Step-by-step explanation:
Given:
[tex]\sqrt{68}[/tex]
To find:
Simplified result of the radical
Solution:
If a value is in square root and it is not a perfect square then we can solve it by finding the answer by factoring down it to smaller factors which are perfect squares and finding the square root of the smaller values
Now
68 can be written as
68 = 2 * 2 * 17
The given is
[tex]\sqrt{68}[/tex]
It can be written as
[tex]\sqrt{68}=\sqrt{2*2*17}[/tex]
=[tex]\sqrt{2^{2}*17}[/tex]
Now
[tex]\sqrt{a.b}[/tex]= [tex]\sqrt{a}[/tex].[tex]\sqrt{b}[/tex]
so given become
[tex]\sqrt{68}=\sqrt{2^{2}}*\sqrt{17}[/tex]
[tex]\sqrt{68}=2*\sqrt{17}[/tex] ∵√2² = 2
[tex]\sqrt{68}=2\sqrt{17}[/tex] ∵a*√b=a√b
