I need help with my algebra hw?

Question

How do you simplyfy the square root of 24, 18, square root of 3 + square root of 3, and the square root of 27 + the square root of 12?

Answer 1

The first thing to do is to find the factors of the number you're taking the root of.
For example, teh factors of 24 include 2*12, 3*8, and 4*6.
Since four is a perfect square (2^2), we'll use that set of factors.
So:
sqrt(24)= sqrt(4*6)= sqrt(4)*sqrt(6)= 2sqrt(6)

Same with sqrt(18):
18=9*2
9=3^2
sqrt(18)= sqrt(9)*sqrt(2)= 3sqrt(2)

sqrt(3) +sqrt(3) can only be reduced by realizing that it's
2*sqrt(3), which could be the sqrt(12). THis is because you can take the two under the radical by squaring it. so you get sqrt (2^2+3)= sqrt(12), but technically 2sqrt(3) is more reduced.

sqrt(27)=3 sqrt(3)
sqrt(12)= 2 sqrt(3)
so 3sqrt(3) + 2sqrt(3) = 5sqrt(3)
in this case, you're treating the sqrt(3) sort of like it was a variable. think of 3x +2x = 5x

Answer 2

√24 = √4√6 = 2√6

√18 = √9√2 = 9√2

√3 + √3 = 2√3

√27 + √12 = √9√3 + √4√3 = 3√3 + 2√3 = 5√3

Answer 3

√24 = 2√6
√18 = 3√2
√3 + √3 = 2√3
√27 + √12 = 3√3 + 2√3 = 5√3

Answer 4

square root of 24 = 2 X square root of 6
becoz sqare root of ab = square root of a X square root of b
Square root of 18 = 3 X Square root of 2
Square root of 3 + Square root of 3 = 2 square root of 3
becoz square root of a + square root of a = 2 X square root of a
sqare root of 27 + square root of 12
= 3 sqaure root of 3 + 2 square root of 3
= 5 square root of 3

Answer 5

Basically, try to find a perfect square in there someplace.

Like sqrt(24) = sqrt(4*6) = sqrt(4) * sqrt(6) = 2*sqrt(6)

Answer 6

24 = 6 * 4 so the sqrtOF24 = sqrtOF6 * sqrtOF4 (which is 2)

so 2 * sqrtOF6 (simplified)

sqrtOF18 = sqrtOF9 * sqrtOF2 = 3 * sqrtOF2

i think you can do the rest

Answer 7

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http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=simplify&s3=basic