Question

5√12 -2√48+2√27упростите выражение

Answer 1

$5 \sqrt{12} -2 \sqrt{12*4} +2 \sqrt{9*3}=5 \sqrt{12}-4 \sqrt{12} +6 \sqrt{3}= \sqrt{12}+6 \sqrt{3}=$ $\sqrt{4*3} +6 \sqrt{3}=2 \sqrt{3} +6 \sqrt{3}=8 \sqrt{3}$

Answer 2

Let's simplify each term under the square root symbol first:

• √12 = √(4 × 3) = 2√3 (we can take out the perfect square factor 4)
• √48 = √(16 × 3) = 4√3 (we can take out the perfect square factor 16)
• √27 = √(9 × 3) = 3√3 (we can take out the perfect square factor 9)

Substituting these values, we have:

5√12 - 2√48 + 2√27 = 5(2√3) - 2(4√3) + 2(3√3)

= 10√3 - 8√3 + 6√3

= (10 - 8 + 6)√3

= 8√3

Therefore, the simplified expression is 8√3.