MATH HELP!!!!!! 20分!!

1) Show that √(2+√3) =√(3/2)+√(1/2).
Sol
√(2+√3)
=√(4+2√3)/√2
=(√3+1)/√2
=√(3/2)+√(1/2)

2)Explain why the equation √(x^2)=x is not valid for all real numbers x and
should be replaced by the equation √(x^2)=｜x｜.
Sol
√(－1)^2=1=｜－１｜，√(－1)^2=1=｜－１｜

3)What is the domain of function (3+x)^1/4?
Sol
3+x>=0
x>=－3

4) Explain why log3＿100 is between 4 and 5.
Sol
81<100<243
log3_81<log3_100<log3_243
log81/log3<log3_100<log243/log3
4<log3_100<5

5) Explain why log with base 0 are not defined.
Sol
p=loga_blogp=bloga
log0 is notdefined

6)Explain why log with a negative base are not defined.
Sol
p=loga_b
logp=bloga
log(－1) is not defined

1)

√(2 + √3)

= √ [√(3/2)² + √(1/2)² + √3 ] .......Since 2 = √(3/2)² + √(1/2)²

= √ [√(3/2)² + √(1/2)² + 2√(3/2)√(1/2)] .....Since √3 = 2√(3/2)√(1/2)

= √ [√(3/2) + √(1/2)]²

= √(3/2) + √(1/2)