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Question

I'm really confused after not taking a math class in 12 years, please help!

1) ^5sqrt sign 1024x^4y^29

2) 9sqrt sign 108 minus 2sqrt sign 147 minus 3sqrt sign 192

Thanks for your help!!

Answer 1

5√(1024x^4 y^29) : original expression
= 5√(16)(16)(2)(2) (x^2)(x^2)(y^14)(y^14)(y) : factor everything under the radical into pairs if possible. All but the last y will pair up.
= 5(16)(2)(x^2)(y^14)√y : bring out one of each pair from under the radical, leaving in this case only the last y under it.
= 160x^2 y^14 √y : multiply it all out, remembering that lonely y still under the radical.

9√108 - 2√147 - 3√192 : original expression
= {9√(6)(6)(3)} - {2 √(7)(7)(3)} - {3√(8)(8)(3)} : factor everything under the radical into pairs if possible. All but the last 3 will pair up.
= {9(6)√3} - {2(7)√3} - {3(8)√3} : bring out one of each pair from under the radical, leaving in this case only the last 3 under it.
= 54 √3 - 14√3 - 24√3 : multiplying out
= (54 - 14 - 24) √3 : common factor of √3, so you can group all numbers together.
This expression simplifies to 16 √3

Answer 2

1) 5sqrt sign 1024x^4y^29
= 5sqrt(64^2x^4y^28)*sqrt(y)
= 5*64x^2y^16sqrt(y)
= 320 x^2y^16sqrt(y)

2) 9sqrt sign 108 minus 2sqrt sign 147 minus 3sqrt sign 192
= 9 sqrt(36*3) - 2sqrt(49*3) - 3 sqrt(64*3)
= 54sqrt(3) - 14sqrt(3) - 24sqrt(3) = 16sqrt(3)