Question

Simplify `11xxsqrt((49a^5)/(4a^3)`?

Answer 1

Solution 2 of 2

Rather than use shortcuts I have given a lot of detail. This is so that you can see where some of the shortcuts come from.

Simplification is `(77a)/2`

Explanation:

You are looking for squared values/variables that can be 'taken outside' the square root.

Demonstrating a property by example:

Suppose we had `sqrt(a/b)` this can be written as `sqrt(a)/sqrt(b)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:`" "11sqrt((49a^5)/(4a^3)`

Write as :`" "11sqrt(49a^5)/sqrt(4a^3)`

`color(green)("For now forget about the 11. Deal with it at the end.")`

Write as:`" "sqrt(7^2xxa^2xxa^2xxa)/sqrt(2^2xxa^2xxa)`

You can cancel some out at this stage. I will do it later.

'Extracting from the root' we have:

`(7xxaxxa)/(2xxa)xxsqrt(a)/sqrt(a)`

This is the same as:

`7/2xxa/axxaxxsqrt(a)/sqrt(a)`

But `a/a=1 and sqrt(a)/sqrt(a)=1` giving

`7/2xx1xxaxx1 color(green)(larr" turning into 1 is the same as cancelling out")`

`(7a)/2`
Now we deal with the 11: `->11xx(7a)/2=(77a)/2`

Answer 2

Solution 1 of 2: using shortcuts
Jumping steps in my head using the principles shown in solution 2 of 2

`11xx(7a)/2=(77a)/2`

Explanation:

Given:`" "11xxsqrt((49a^5)/(4a^3)`

`11xxsqrt((49a^(5-3))/(4)`

`(77a)/2`