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

2 Answers
Apr 6, 2017

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 $\frac{77 a}{2}$

Explanation:

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

Demonstrating a property by example:

Suppose we had $\sqrt{\frac{a}{b}}$ this can be written as $\frac{\sqrt{a}}{\sqrt{b}}$
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Given:" "11sqrt((49a^5)/(4a^3)

Write as :$\text{ } 11 \frac{\sqrt{49 {a}^{5}}}{\sqrt{4 {a}^{3}}}$

$\textcolor{g r e e n}{\text{For now forget about the 11. Deal with it at the end.}}$

Write as:$\text{ } \frac{\sqrt{{7}^{2} \times {a}^{2} \times {a}^{2} \times a}}{\sqrt{{2}^{2} \times {a}^{2} \times a}}$

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

'Extracting from the root' we have:

$\frac{7 \times a \times a}{2 \times a} \times \frac{\sqrt{a}}{\sqrt{a}}$

This is the same as:

$\frac{7}{2} \times \frac{a}{a} \times a \times \frac{\sqrt{a}}{\sqrt{a}}$

But $\frac{a}{a} = 1 \mathmr{and} \frac{\sqrt{a}}{\sqrt{a}} = 1$ giving

$\frac{7}{2} \times 1 \times a \times 1 \textcolor{g r e e n}{\leftarrow \text{ turning into 1 is the same as cancelling out}}$

$\frac{7 a}{2}$
Now we deal with the 11: $\to 11 \times \frac{7 a}{2} = \frac{77 a}{2}$

Apr 6, 2017

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

$11 \times \frac{7 a}{2} = \frac{77 a}{2}$

Explanation:

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

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

$\frac{77 a}{2}$