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# Which expression is equal to 2√54−4√24?

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Which expression is equal to 2√54−4√24?

A. -√6

B. -2√6

C. -11√6

D. √6

Sep 15, 2017

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Simplify the following:
2 sqrt(54) - 4 sqrt(24)

sqrt(54) = sqrt(2×3^3) = 3 sqrt(2) sqrt(3):
2×3 sqrt(2) sqrt(3) - 4 sqrt(24)

Hint: | For a>=0, sqrt(a) sqrt(b) = sqrt(a b). Apply this to sqrt(2) sqrt(3).
sqrt(2) sqrt(3) = sqrt(2×3):
2×3 sqrt(2×3) - 4 sqrt(24)

Hint: | Multiply 2 and 3 together.
2×3 = 6:
2×3 sqrt(6 ) - 4 sqrt(24)

sqrt(24) = sqrt(2^3×3) = 2 sqrt(2) sqrt(3):
2×3 sqrt(6) - 42 sqrt(2) sqrt(3)

Hint: | For a>=0, sqrt(a) sqrt(b) = sqrt(a b). Apply this to sqrt(2) sqrt(3).
sqrt(2) sqrt(3) = sqrt(2×3):
2×3 sqrt(6) - 4×2 sqrt(2×3)

Hint: | Multiply 2 and 3 together.
2×3 = 6:
2×3 sqrt(6) - 4×2 sqrt(6 )

Hint: | Multiply 2 and 3 together.
2×3 = 6:
6 sqrt(6) - 4×2 sqrt(6)

Hint: | Multiply -4 and 2 together.
-4×2 = -8:
6 sqrt(6) + -8 sqrt(6)

Hint: | Combine like terms in 6 sqrt(6) - 8 sqrt(6).
6 sqrt(6) - 8 sqrt(6) = -2 sqrt(6):
= -2 sqrt(6)

Sep 15, 2017

#1
0

Simplify the following:
2 sqrt(54) - 4 sqrt(24)

sqrt(54) = sqrt(2×3^3) = 3 sqrt(2) sqrt(3):
2×3 sqrt(2) sqrt(3) - 4 sqrt(24)

Hint: | For a>=0, sqrt(a) sqrt(b) = sqrt(a b). Apply this to sqrt(2) sqrt(3).
sqrt(2) sqrt(3) = sqrt(2×3):
2×3 sqrt(2×3) - 4 sqrt(24)

Hint: | Multiply 2 and 3 together.
2×3 = 6:
2×3 sqrt(6 ) - 4 sqrt(24)

sqrt(24) = sqrt(2^3×3) = 2 sqrt(2) sqrt(3):
2×3 sqrt(6) - 42 sqrt(2) sqrt(3)

Hint: | For a>=0, sqrt(a) sqrt(b) = sqrt(a b). Apply this to sqrt(2) sqrt(3).
sqrt(2) sqrt(3) = sqrt(2×3):
2×3 sqrt(6) - 4×2 sqrt(2×3)

Hint: | Multiply 2 and 3 together.
2×3 = 6:
2×3 sqrt(6) - 4×2 sqrt(6 )

Hint: | Multiply 2 and 3 together.
2×3 = 6:
6 sqrt(6) - 4×2 sqrt(6)

Hint: | Multiply -4 and 2 together.
-4×2 = -8:
6 sqrt(6) + -8 sqrt(6)

Hint: | Combine like terms in 6 sqrt(6) - 8 sqrt(6).
6 sqrt(6) - 8 sqrt(6) = -2 sqrt(6):
= -2 sqrt(6)

Guest Sep 15, 2017