Simplify the following:
2 sqrt(2)×3 sqrt(3)×5 sqrt(12)
sqrt(12) = sqrt(2^2×3) = 2 sqrt(3):
2 sqrt(2)×3 sqrt(3)×5×2 sqrt(3)
2 sqrt(2)×3 sqrt(3)×5×2 sqrt(3) = 2 sqrt(2)×2×3^(1+1/2+1/2)×5:
2 sqrt(2)×2×3^(1+1/2+1/2)×5
Put 1+1/2+1/2 over the common denominator 2. 1+1/2+1/2 = 2/2+1/2+1/2:
2 sqrt(2)×2×3^2/2+1/2+1/2×5
2/2+1/2+1/2 = (2+1+1)/2:
2 sqrt(2)×2×3^(2+1+1)/2×5
2+1+1 = 4:
2 sqrt(2)×2×3^(4/2)×5
The gcd of 4 and 2 is 2, so 4/2 = (2×2)/(2×1) = 2/2×2 = 2:
2 sqrt(2)×2×3^2×5
3^2 = 9:
2 sqrt(2)×2×9×5
2×2 = 4:
4×9×5 sqrt(2)
4×9 = 36:
36×5 sqrt(2)
36×5 = 180:
Answer: | 180 sqrt(2)
+128578 2sqrt(2) * 3sqrt(3) * 5sqrt(12)
2 √ 2 * 3 √3 * 5 √12 and since we're multiplying....we can switch the order any way we would like......so we have.....
[ 2 * 3 * 5 ] * [ √2 * √3 * √12 ]
[ 30] * [ √2 * √3 * √4 * √3 ]
[30] * [ √2 * √3 * 2 * √3 ]
[30 *2] * [ √3 * √3 * √2 ]
60 * [ 3 * √2 ]
60 * 3 * √2
180 √2
