Simplify the square root of (54x^9*y^7)?

√(54x⁹y⁷) = √(9·6x⁸xy⁶y)
= √9√x⁸√y⁶√(6xy)
= 3x⁴y³√(6xy)

√ (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)

(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).

3 √6 x^(9/2) y^(7/2)

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)