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Xelga [282]
3 years ago
12

Someone help me with this I will make you brain

Mathematics
1 answer:
hram777 [196]3 years ago
5 0

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.

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