My kids are squabbling over this.

My girl gave the same answer as the Solution Key, which is 24+8*(square root of 2)+3*(square root of 3)+(square root of 6), everything over 7.

My son was bothered by that square root of 6 left untouched, and factored it as (square root of 2)*(square root of 3). Then he factored that whole numerator by grouping: he factored 8 out of the first two terms, so he got 8*(3+square root of 2), then he factored the square root of 3 out of the other two terms, and he got (square root of 3)*(3+square root of 2). Then he factored (3+square root of 2), and his final answer was as follows: (3+square root of 2)(8+square root of 3), everything over 7.

I'm siding with my son. Who's right?

Thank you!

My girl gave the same answer as the Solution Key, which is 24+8*(square root of 2)+3*(square root of 3)+(square root of 6), everything over 7.

My son was bothered by that square root of 6 left untouched, and factored it as (square root of 2)*(square root of 3). Then he factored that whole numerator by grouping: he factored 8 out of the first two terms, so he got 8*(3+square root of 2), then he factored the square root of 3 out of the other two terms, and he got (square root of 3)*(3+square root of 2). Then he factored (3+square root of 2), and his final answer was as follows: (3+square root of 2)(8+square root of 3), everything over 7.

I'm siding with my son. Who's right?

Thank you!

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