+0  
 
0
41
1
avatar

Simplify the following expression to a simplified fraction: 

 

\(\sqrt{\dfrac{\dfrac{5}{\sqrt{20}}+\dfrac{\sqrt{845}}{9}+\sqrt{5}}{\sqrt5}}\)

 May 17, 2022
 #1
avatar+1768 
+1

We will start with the numerator of the square root. 

 

For the first fraction(\(\large{5 \over {\sqrt {20}}}\)), we can rationalize the denominator, by multiplying the fraction by \(\large{\sqrt {20 } \over {\sqrt{20}}}\). This gives us \(\large{{5 \sqrt {20 }} \over 20}\)

We can rewrite \(\sqrt{20}\) as \(2 \sqrt 5 \). This means we have \(\large{5 \times 2 \sqrt 5 \over 20}\), which simplifies to \(\large{\sqrt 5 \over 2}\)

Repeating this process to the second fraction (\(\large{\sqrt{845} \over 9}\)) gives us \(\large{{13 \sqrt 5} \over 9}\)

Adding all the terms up gives us: \(\large{{{26 \sqrt5}\over 18} + {18\sqrt5 \over 18} + {9 \sqrt 5 \over 18}} = {53 \sqrt 5 \over 18}\).

This means that we have: \(\large{\sqrt{{53 \sqrt5 \over 18} \over \sqrt 5}}\)

Now, we just have to cancel out the common terms, and we have our answer. 

 

Can you take it from here?

 May 17, 2022

13 Online Users

avatar