Math Help needed

Question

1) Simplify the expression and show the check of your answer. Assume that x and y represent nonnegative real numbers.

√(64x^12 y^20 )


2) Simplify the expression. Assume that x and y represent nonnegative real numbers.

∛((-27y^48)/(81x^4 ))











3) Simplify the expression. Assume that x represent nonnegative real number.

9√(27x^2 )-14√(108x^2 )+2√(48x^2 )












4) Perform the indicated operations and simplify if possible:

(√(x+3)-4)^2










5) Perform the indicated operations and simplify your answer.

(√21-√5)^2

Answer 1

√(64x¹²y²⁰)

= [8²(x⁶)²(y¹⁰)²]

= 8x⁶y¹⁰

 

³√[(-27y⁴⁸)/(81x⁴)]

= ³√[(-3y¹⁶)³/((3)(3³)(x)(x³))]

= (-3y¹⁶)/[(3x)( ³√(3x))]

= -y¹⁶/[x(³√3x)]

 

9√(27x²) - 14√(108x²) + 2√(48x²)

 

= 9√[3²(3)x²] - 14√(6²(3)x²) + 2√4²(3)x²

 

= 9(3x)√3 - 14(6x)√3 + 2(4x)√3

 

= 27x√3 - 84x√3 + 8x√3

 

= (27x - 84x + 8x)√3

 

= -49x√3

 

***************************

try the last two using:

(a + b)² = a^2 + 2ab + b^2

(a - b)^2 = a^2 - 2ab + b^2