Question

How can you write the expression below with a rationalized denominator sqrt3-sqrt6/sqrt3+sqrt6

Answer 1

1. 10^4√2x

2. 3√10 units

3. 10∛6

4. -49 + 13 √7

5. -3 + 2√2

this is the whole quick check.

Answer 2

Rewriting the given expression by rationalizing the denominator we proceed as follows:
[√3-√6]/[√3+√6]
to rationalize the denominator we multiply the numerator and the denominator by the conjugate. Thus we shall have:
[√3-√6]/[√3+√6]×[√3-√6]/[√3-√6]
={√3(√3-√6)-√6(√3-√6)}/{√3(√3+√6)-√6(√3+√6)}
=[3-√3√6-√3√6+6]/[3+√3√6-√3√6-6]
simplifying the above we obtain:
[3-2√18+6]/[3-6]
=[3+6-6√2]/(-3)
=[9-6√2]/(-3)
=2√2-3
Answer: 2√2-3