1、1二次根式的运算解答题1.计算:(1) ;(2)- ;(-144)(-169)13225(3)- ;(4) (m0,n0).121 0245 182解析 (1)原式= = =1213=156.144169144 169(2)原式=- 15=-5.13(3)原式=- =- 32 =-16 .123225 12 5 5(4)原式= =3m .3222 22.计算:(1) ;(2) ;(-7 314)2 (- 1-2425)2(3) (-9 );(4) ;2333445 (-7128) (-13126)(5)4 + - +4 ;(6)6-2 -35 45 8 232 32.解析 (1)原式=49 =
2、 .(2)原式=1- = .314212 2425125(3)原式= (-27 )=- 27 =-45 .231545 153 5 3(4)原式= = = = .4928 1269 74147224 722(5)原式=4 +3 -2 +4 =7 +2 .5 5 2 2 5 2(6)原式=6- - =6- .6362 5623.计算:(1) + -4 ;22-11812(2)(5 -6 +4 ) ;48 27 15 3(3) + +(-2)-2;18( 2+1)-1(4) + - .23-127( 3-1)0解析 (1)原式=2( +1)+3 -4 =2 +2+3 -2 =2+3 .2 222
3、2 2 2 22(2)原式=(54 -63 +4 ) =(2 +4 ) =2+4 .3 3 15 3 3 15 3 5(3)原式=3 + + =3 + -1+ =4 - .212+1142 2 14 234(4)原式= +1+3 -1=4 .3 3 34.计算:(1) ;15(1+ 52 )2-(1- 52 )2(2) a2b2 ;(2-+) (3) ( + )+( + ) .6 3 2 3 2 6解析 (1)原式= = =1.15(1+ 52 +1- 52 )(1+ 52 -1- 52 ) 155(2)原式= (2-+1) 122 = = mn= .2-+1 1222-+122 2-+122
4、(3)原式= + = + =3 -2 + + = - .63+ 2 3+ 26 6( 3- 2)( 3+ 2)(3- 2) ( 3+ 2) 66 62 312 213 372 253 35.先化简,再求值: ,其中 a=3,b=4.4( + )(- )+ + ( - ) - 解析 原式= - 4( + )(- ) ( + )2( + )(- ) - = -( - )2( + )(- ) - =- =- = .1+ - - - -当 a=3,b=4 时,原式= = -2.4- 33-4 36.已知 a= -1,求 的值.17 (5+24-173-2+18-17)2 017解析 a= -1,a+1= ,(a+1) 2 =17.17 17原式=a 5+2a4-(a+1)2a3-a2+(a+1)2+1a-(a+1)22 017=5+24-(5+24+3)-2+(2+2+2)-2-2-12 017= =(-1)2 017=-1.(-3-2+3+22+2-2-2-1)2 0173
