Final answer:
The simplified form of the expression 2V2•7V18 is 84. This result is obtained by multiplying the coefficients and the radicands of the square roots independently and then simplifying the product of the radicands, which is a perfect square.
Step-by-step explanation:
The student asked what the expression 2V2•7V18 simplifies to. This expression involves the multiplication of square roots and can be simplified step by step:
- First, write the expression with square root signs: 2√2 × 7√18.
- Next, multiply the coefficients (the numbers outside the square root signs): 2 × 7 = 14.
- Now, multiply the numbers under the square root signs (the radicands): √2 × √18 = √(2×18) = √36.
- √36 is a perfect square and is equal to 6.
- Combine the two results: 14×6 which equals 84.
- So the simplified form of the expression is not listed among the provided options. It is actually 84.
The correct answer to this problem is not provided among the options (a) 14V36, (b) 14V20, (c) 7V36, or (d) 7V20.