Question

Combine the radicals 5 √27-17√3.
A) 2 √24}
B) 28√3}
C) 3√2
D) -2√3}

Answer 1

The radicals 5 √27 and -17√3 combine to simplify to -2√3 upon simplification of √27 to 3√3 and multiplication by 5, then subtracting 17√3. The correct answer is option D.

Step-by-step explanation:

Combining Radicals

To combine the radicals 5 √27 and -17√3, we first look for opportunities to simplify the square roots. The number 27 can be expressed as 3³, which means √27 is the same as √(3³) or 3√3. Now we can rewrite the expression as 5 × 3√3 - 17√3.

After simplifying, we multiply 5 by 3 to get the coefficient for √3, resulting in 15√3. Then we subtract 17√3 from 15√3, giving us (15 - 17)√3, which simplifies to -2√3.

Therefore, the expression 5 √27 - 17√3 simplifies to -2√3, which corresponds to choice D in the list of options provided.