Mathematics, 01.08.2019 00:00 jadfavors4321

Can you me simplify these double radicals? 1. $\sqrt{6+2 \sqrt{5} }$ 2. $\sqrt{6+2 \sqrt{8} }$ 3. $\sqrt{10+2 \sqrt{21} }$ 4. $\sqrt{7-2 \sqrt{10} }$ 5. $\sqrt{10-2 \sqrt{21} }$ 6. $\sqrt{6-\sqrt{20} }$ 7. $\sqrt{7-\sqrt{48} }$ 8. $\sqrt{8+4\sqrt{3} }$ 9. $\sqrt{12-6\sqrt{3} }$ 10. $\sqrt{19+8\sqrt{3} }$

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You know that
.. (a +b)^2 = a^2 +b^2 +2ab
If these are square roots, then you have
.. (√a +√b)^2 = a +b +2√(ab)
.. (√a -√b)^2 = a +b -2√(ab)

In each case, you can put the inner radical in the form 2√something, then look for two factors of "something" that add to the other constant.
The result is then √factor1 ±√factor2, with the sign matching that under the original radical.

1. 1 +√5
2. 2 +√2
3. √3 +√7
4. √5 -√2 . . . . . . . . Technically, √(x^2) = |x|. By expressing the result as a positive number (smaller subtracted from larger), we don't have to worry about absolute value.

5. See 3 and 4. √7 -√3
6. √20 = 2√5. See 1 and 4.
.. √5 -1
7. 2 -√3
8. 4√3 = 2√12 = 2√(6*2)
.. √6 +√2
9. 6√3 = 2√(9*3)
.. 3 -√3
10. 8√3 = 2√(16*3)
.. 4 +√3

Answer from: Quest

answer: segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students. an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality. in the case of brown v. board of education, that standard was challenged and defeated. segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to education. this was being violated by states whose laws supported the segregation of schools. section 1 of the 14th amendment reads as follows:

all persons born or naturalized in the united states and subject to the jurisdiction thereof, are citizens of the united states and of the state wherein they reside. no state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the united states; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.

Answer from: Quest

option 1

data plot with 3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.

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