Question

Could someone please explain why and how to simplify the following radicals

1) √63

2)√96

3)√x^23

4)√40x^5y

Answer 1

\[\sqrt{63}\]=\[\sqrt{63}= \sqrt{9\times7} =\sqrt{3^{2}\times7} = 3\times \sqrt{7}\]

Answer 2

Great, how did you get it?

Answer 3

\[\sqrt{96} = \sqrt{16\times6} = \sqrt{4^{2}\times2\times3} = 4\times \sqrt{3}\times \sqrt{2}\]

Answer 4

To get it think about the given number as the product of square numbers with other numbers 9,16 are square numbers

Answer 5

3rd one there is no radical sign check it

Answer 6

4th one do u mean sqrt(40*x^5*y) or sqrt(40*x^(5y)) ?

Answer 7

I don't really need the equations done because I've already done them. I just need to write sentences explaining how I got them and why, which I'm not good at explaining. Fixed #3

Answer 8

Yes for the 4th one the 5 is on top of the x and the y is still on the bottom

Answer 9

\[\sqrt{x^23} = x^{23/2} =x ^{11.5}\]

Answer 10

\[\sqrt{40\times x ^{5}\times y} = \sqrt{8\times 5\times x ^{5}\times y} = \sqrt{2^{3} \times 5 \times x ^{5}\times y} = 2\times \sqrt{2} \times x ^{2.5} \times y ^{0.5}\]

Answer 11

sry i missed a sqrt(5) there u should have to multiply the final answer by sqrt(5)

Answer 12

I don't need the math done, I've already done that. I need sentences explaining how and why I got √7 for number one, 4x√3x√2 for number 2, etc.

Answer 13

caz 2,3,5,7,11,13,.... these are prime numbers u can factorize any number upto its pime factors that why they r coming

Answer 14

Actually here i factorized them and took the radical simple as that