Step-by-step explanation:
let's look at the full numbers under the square roots when bringing the external factors back in :
sqrt(9×9×2) - sqrt(3×3×7) + sqrt(8) - sqrt(28)
and let's present these numbers as the product of their basic prime factors
sqrt(3×3×3×3×2) - sqrt(3×3×7) + sqrt(2×2×2) - sqrt(2×2×7)
now we see that we have 2 pairs of square roots : 1 pair ends with a factor of 2, and one pair with a factor of 7.
let's combine these
sqrt (3×3×3×3×2) + sqrt(2×2×2) - sqrt(3×3×7) - sqrt (2×2×7)
and now we move the factors of 2 and 7 back out in front (of course, we need to apply the square root on these factors) :
9×sqrt(2) + 2×sqrt(2) - 3×sqrt(7) - 2×sqrt(7) =
= (9+2)×sqrt(2) - (3+2)×sqrt(7) = 11×sqrt(2) - 5×sqrt(7)
and that is the first answer option.
Can you post the rest of the question please?
Answer:
-3
Step-by-step explanation:
<span>The long piece should measure 7.5 feet or 7'6" (7 foot 6 inches).
If x is the length of the short piece then the length of the long piece must be 3x. The total length of the uncut beam is 10 foot.
This can be represented by :
x + 3x = 10
4x = 10
x = 2.5
As x = 2.5 = length of short piece, then the long piece measures 3x = 3(2.5) = 7.5 feet.
There are 12 inches in a foot so 7.5 feet = 7'6"</span>
