Question

What is √10/√3 in simplest radical form?
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Answer 1

sqrt30/3

Explanation:

Took the quiz at k12 and got it correct :)

Answer 2

The first thing we need to do is to multiply both numerator and denominator by
`√(3)` so that the denominator is not a radical any more:

thus, we have
`\displaystyle{ ( √(10) )/( √(3)) \cdot ( √(3) )/( √(3))= ( √(10) \cdot √(3) )/(( √(3) )^2)`.

Now, applying the rules (i)
`\sqrt{ x^(2) }=x` (for x≥0) and (ii)
`√(a) \cdot √(b) = √(ab)`, we have:


`\displaystyle{ ( √(10) \cdot √(3) )/(( √(3) )^2)= ( √(30) )/(3)`.


Answer:
`\displaystyle{ ( √(30) )/(3)`