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# builderboi help

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Simplify the following expression to a simplified fraction:

$$\sqrt{\dfrac{\dfrac{5}{\sqrt{20}}+\dfrac{\sqrt{845}}{9}+\sqrt{5}}{\sqrt5}}$$

May 17, 2022

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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