Question

Solve each questions by taking square roots

1.k²=76
2.k²=16
3.x²=21
4.a²=40
5.x²+8=28
6.2n²=-144
7.-6m²=-414
8.7x²=-21
9.m²+7=88
10.-5x²=-500
11.-7n²=-448
12.-2k²=-162
13.x²-5=73
14.16n²=49

Answer 1

`1.\ k^2=76\\\\k=\pm√(76)\\\\k=\pm√(4\cdot19)\\\\k=\pm2√(19)\\-------------\\2.\ k^2=16\\\\k=\pm√(16)\\\\k=\pm4\\-------------\\`

`3.\ x^2=21\\\\x=\pm√(21)\\-------------\\4.\ a^2=40\\\\a=\pm√(40)\\\\a=\pm√(4\cdot10)\\\\a=\pm2√(10)\\-------------\\5.\ x^2+8=28\ \ \ /-8\\\\x^2=20\\\\x=\pm√(20)\\\\x=\pm√(4\cdot5)\\\\x=\pm2\sqrt5\\-------------\\`

`6.\ 2n^2=-144\ \ \ \ /:2\\\\n^2=-72-no\ real\ solutions\\-------------\\7.\ -6m^2=-414\ \ \ \ /:(-6)\\\\m^2=69\\\\m=\pm√(69)\\-------------\\8.\ 7x^2=-21\ \ \ \ /:(-7)\\\\x^2=-3-no\ real\ solutions\\-------------\\`

`9.\ m^2+7=88\ \ \ \ /-7\\\\m^2=88-7\\\\m^2=81\\\\m=\pm√(81)\\\\m=\pm9\\-------------\\10.\ -5x^2=-500\ \ \ \ /:(_5)\\\\x^2=100\\\\x=\pm√(100)\\\\x=\pm10\\-------------\\`

`11.\ -7n^2=-448\ \ \ \ /:(-7)\\\\n^2=64\\\\n=\pm√(64)\\\\n=\pm8\\-------------\\12.\ -2k^2=-162\ \ \ \ /:(-2)\\\\k^2=81\\\\k=\pm√(81)\\\\k=\pm9\\-------------\\`

`13.\ x^2-5=73\ \ \ \ /+5\\\\x^2=78\\\\x=\pm√(78)\\-------------\\14.\ 16n^2=49\ \ \ \ /:16\\\\n^2=(49)/(16)\\\\n=\pm\sqrt(49)/(16)\\\\n=\pm(√(49))/(√(16))\\\\n=\pm(7)/(4)`