How do I divide 3sqrt40 by 3sqrt5?
sqrt40=sqrt(5*2*4)=2sqrt5*sqrt2
3√40
-----------
3√5
√40
=-----------
√5
=√(40/5)
=√8
=√2^2*2
=2√2
To divide 3√40 by 3√5, we can simplify the expression by applying the rules of radicals.
Step 1: Simplify the Radicals
First, let's simplify the radicals inside the square root symbols:
√40 = √(4 × 10) = √4 × √10 = 2√10
√5 remains as it is since it cannot be simplified further.
Step 2: Rewrite the Expression
Now, we can rewrite the expression in a simplified form:
3√40 = 3 × 2√10 = 6√10
3√5 will remain as it is.
Step 3: Divide the Radicals
Finally, we can divide the radicals:
(6√10) / (3√5) = 6/3 × √10/√5 = 2 × √(10/5) = 2 × √2 = 2√2
So, the simplified result of dividing 3√40 by 3√5 is 2√2.