Question

Distribute and simplify these radicals. 2√3· (√2+√3)

A. 2√6+6
B. 2√15
C. 30
D. 6√2+6

Answer 1

The correct answer is option A. Distributing and simplifying 2√3· (√2+√3) involves using the distributive property. This gives us 2√6 when multiplied with √2 and 6 when multiplied with √3. The simplified expression is 2√6 + 6, which corresponds to option A.

Step-by-step explanation:

To distribute and simplify the radicals in the expression 2√3· (√2+√3), we need to apply the distributive property. The distributive property states that a(b + c) = ab + ac. Here, our 'a' is 2√3, 'b' is √2, and 'c' is √3.

We multiply 2√3 by √2 to get 2√(3×2) or 2√6. Next, we multiply 2√3 by √3 to get 2√(3×3) or 2·3, which simplifies to 6.

Combining both terms we get 2√6 + 6. Hence, the correct option is A. 2√6 + 6.