Answer options are
A) 3x^4*y^3 square roots of 6
B) 3x^4*y^3 square roots of 6xy
C) 9x^4*y^3 square roots of 6xy
D) 9x^3*y^3 square roots of 6xy
Simplify the square root of (54x^9*y^7)?
回答 (5)
2017-09-28 12:10 am
✔ 最佳答案
√(54x⁹y⁷) = √(9·6x⁸xy⁶y)= √9√x⁸√y⁶√(6xy)
= 3x⁴y³√(6xy)
2017-09-28 12:03 am
√ (54 x⁹ y⁷)
= √ [(3² * 6) * (x⁸ * x) * (y⁶ * y)]
= √ [3² * 6 * (x⁴)² * x * (y³)² * y]
= (3 * x⁴ * y³) √ (6 * x * y)
= 3 x⁴ y³ √ (6 x y)
The answer: B. 3 x⁴ y³ √ (6 x y)
= √ [(3² * 6) * (x⁸ * x) * (y⁶ * y)]
= √ [3² * 6 * (x⁴)² * x * (y³)² * y]
= (3 * x⁴ * y³) √ (6 * x * y)
= 3 x⁴ y³ √ (6 x y)
The answer: B. 3 x⁴ y³ √ (6 x y)
2017-09-28 12:17 am
(54 * x^9 * y^7)^(1/2) =
= (54)^(1/2) * (x^9)^(1/2) * (y^7)^(1/2) =
= [(2) * (3^3)]^(1/2) * (x)^(9/2) * y^(7/2) =
= (2)^(1/2) * 3^(3/2) * (x)^(8/2) * (x)^(1/2) * (y)^(6/2) * (y)^(1/2) =
= (2)^(1/2) * 3^(2/2) * 3^(1/2) * (x)^(8/2) * (x)^(1/2) * (y)^(6/2) * (y)^(1/2) =
= √2 * 3 * √3 * x^4 * √x * y^3 * √y =
= (√2 * √3) * 3 * (√x * √y) * x^4 * y^3 =
= √6 * 3 * √(xy) * x^4 * y^3 =
= 3 * x^4 * y^3 * √(6xy).
Answer: B).
= (54)^(1/2) * (x^9)^(1/2) * (y^7)^(1/2) =
= [(2) * (3^3)]^(1/2) * (x)^(9/2) * y^(7/2) =
= (2)^(1/2) * 3^(3/2) * (x)^(8/2) * (x)^(1/2) * (y)^(6/2) * (y)^(1/2) =
= (2)^(1/2) * 3^(2/2) * 3^(1/2) * (x)^(8/2) * (x)^(1/2) * (y)^(6/2) * (y)^(1/2) =
= √2 * 3 * √3 * x^4 * √x * y^3 * √y =
= (√2 * √3) * 3 * (√x * √y) * x^4 * y^3 =
= √6 * 3 * √(xy) * x^4 * y^3 =
= 3 * x^4 * y^3 * √(6xy).
Answer: B).
2017-09-28 12:03 am
3 √6 x^(9/2) y^(7/2)
2017-09-27 11:58 pm
sqrt(54x^9y^7)
is the same as
sqrt(54) times sqrt(x^9) times sqrt(y^7)
is the same as
sqrt(9) times sqrt(6) times sqrt(x^8) times sqrt(x^1) times sqrt(y^6) times sqrt(y^1)
3 times sqrt(6) times x^(8/2) times sqrt(x) times y^(6/2) times sqrt(y)
3 times sqrt(6xy) times x^4 times y^3
3x^4y^3 times sqrt(6xy)
is the same as
sqrt(54) times sqrt(x^9) times sqrt(y^7)
is the same as
sqrt(9) times sqrt(6) times sqrt(x^8) times sqrt(x^1) times sqrt(y^6) times sqrt(y^1)
3 times sqrt(6) times x^(8/2) times sqrt(x) times y^(6/2) times sqrt(y)
3 times sqrt(6xy) times x^4 times y^3
3x^4y^3 times sqrt(6xy)
收錄日期: 2021-04-18 17:49:56
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