Combine the following expressions. $$ -\sqrt{147}+\sqrt{192}-\sqrt{243} $$ $$ -3 \sqrt{8} $$ $$ 8 \sqrt{3} $$ $$ -8 \sqrt{3} $$

Question

UpStudy AI · Accepted Answer

We'll simplify each term before combining.

1. For the first group:
  –√147 + √192 – √243

• √147 = √(49×3) = 7√3, so –√147 = –7√3.
  • √192 = √(64×3) = 8√3.
  • √243 = √(81×3) = 9√3, so –√243 = –9√3.

Thus, –7√3 + 8√3 – 9√3 = (–7 + 8 – 9)√3 = –8√3.

2. The second term:
  –3√8
  • √8 = √(4×2) = 2√2, so –3√8 = –3×2√2 = –6√2.

3. The third and fourth terms:
  8√3 and –8√3
  These cancel each other: 8√3 – 8√3 = 0.

Now, combine all simplified parts:
  –8√3 (from the first group) + (–6√2) + 0 = –6√2 – 8√3.

The final combined expression is: –6√2 – 8√3.
The combined expression is $$ -6\sqrt{2} - 8\sqrt{3} $$.

Combine the following expressions. \( -\sqrt{147}+\sqrt{192}-\sqrt{243} \) \( -3 \sqrt{8} \) \( 8 \sqrt{3} \) \( -8 \sqrt{3} \)