Question

数学高手来！！！

化简

Answer 1

(1)先内面展开
=根号（16+2+2根号5+4根号3+4根号15)=根号（18+2(根号5+根号12）+2根号5*根号12）
因为17+2根号5*根号12=(根号5+根号12)^2
所以上式=根号[(根号5+根号12)^2+2(根号5+根号12)+1]=根号5+根号12+1

(2)从内到外逐渐化简
因为13+根号48=13+2根号12*1=(1+根号12)^2
4-根号12=4-2根号3*1=(根号3-1)^2
所以原式=根号（2+根号3）/(根号6+根号2）=根号（4+2根号3）/(2根号3+2）=1/2

追问

根号（2+根号3）/(根号6+根号2）=根号（4+2根号3）/(2根号3+2）=1/2 (why)详细点嘛

Answer 2

(1) = ( (1+2*3^(1/2)+5^(1/2))^2 )^(1/2) = 1 + 2*3^(1/2) + 5^(1/2)

(2) = ((3^(1/2) + 1)^2 /2^(1/2))^(1/2) / (2^(1/2) = 1/2

追问

^这是什么意思啊

追答

^ power
2^4 = 2* 2 * 2 * 2
3^(-2) = 1/(3*3) = 1/9

追问

好多地方看不懂，能详细点吗，要分的话我有的都可以给你

追答

this problem is too long . u can just check my answer.

for example, ( 13 + 48^(1/2) )^(1/2) = ( 12 + 2*12^(1/2) )^(1/2)
= ( (12^(1/2))^2 + 2 * 12^(1/2) * 1 + 1^2 )^(1/2)
= ( ( 12^(1/2) + 1 )^2 ) ^(1/2)
= 12^(1/2) + 1

you have 4 computations like this one.