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cricket20 [7]
2 years ago
6

What is the square root of 5 divided by the square root of 15 and simplify and in fraction form​

Mathematics
1 answer:
ozzi2 years ago
4 0

Answer:

\sqrt{\frac{1}{3} }

or

\frac{\sqrt{3} }{3}

Step-by-step explanation:

The expression \frac{\sqrt{5} }{\sqrt{15} } can be simplified by first writing the fraction under one single radical instead of two.

\frac{\sqrt{5} }{\sqrt{15} } = \sqrt{\frac{5}{15} }

5/15 simplifies because both share the same factor 5.

It becomes \sqrt{\frac{5}{15} } = \sqrt{\frac{1}{3} }

This can simplify further by breaking apart the radical.

\sqrt{\frac{1}{3} }  = \frac{\sqrt{1} }{\sqrt{3} }  = \frac{1}{\sqrt{3} }

A radical cannot be left in the denominator, so rationalize it by multiplying by √3 to numerator and denominator.

\frac{1}{\sqrt{3} } *\frac{\sqrt{3} }{\sqrt{3} }  =\frac{\sqrt{3} }{3}

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