2*sqrt(12) + sqrt(27) = 2*sqrt(4*3) +sqrt(9*3) = 2*sqrt(4)*sqrt(3) + sqrt(9)*sqrt(3) = 2*2*sqrt(3) + 3*sqrt(3) = 4*sqrt(3) + 3*sqrt(3) = 7*sqrt(3)
28/sqrt(8) multiply top and bottom by sqrt(8) = 28*sqrt(8)/[sqrt(8)*sqrt(8)] = 28*sqrt(8)/8 = 7*sqrt(8)/2 But sqrt(8) = sqrt(4*2)= sqrt(4)*sqrt(2) = ±2*sqrt(2) then 7*sqrt(8)/2 = ±7*2*sqrt(2)/2 = ±7*sqrt(2)
1/[5 + 3*sqrt(2)] = [5 - 3*sqrt(2)]/{[5 + 3*sqrt(2)][5 - 3*sqrt(2)]} = [5 + 3*sqrt(2)]/[25 - 18] = [5 - 3*sqrt(2)]/7
Approximately 2.828427
84
sqrt(28) + sqrt(63) =sqrt(7 x 4) + sqrt(7 x 9) =[ sqrt(7) x sqrt(4) ] + [ sqrt(7) x sqrt(9) ] =2 sqrt(7) + 3 sqrt(7) =5 sqrt(7) = 13.229 (rounded)
It will depend on where you put your parentheses. Root 7 -( 1/root 7) is different from (root 7-1)/root 7. * * * * * True, but a more helpful answer: [sqrt(7) - 1]/[sqrt(7) + 1] - [sqrt(7) + 1]/[sqrt(7) - 1] Multiplying the numerator and denominator of the first fraction by [sqrt(7) - 1] and the second fraction by [sqrt(7) + 1] = [sqrt(7) - 1]2/[7 - 1] - [sqrt(7) + 1]2/[7 - 1] =[7 - 2*sqrt(7) + 1]/6 - [7 + 2*sqrt(7) + 1]/6 = 16/6 = 8/3
2w2 + 22w + 7 = 0 w = [-22 +/- sqrt(22*22 - 4*2*7)] / (2*2) = [-22 +/- sqrt(484 - 56)] / 4 = [-22 +/- sqrt(428)] / 4 so w = -0.328 or w = -10.672
(sqrt(9) - sqrt(12) + sqrt(16)) x sqrt(2) = -2 sqrt(6) + 7 sqrt(2)
2*sqrt(12) + sqrt(27) = 2*sqrt(4*3) +sqrt(9*3) = 2*sqrt(4)*sqrt(3) + sqrt(9)*sqrt(3) = 2*2*sqrt(3) + 3*sqrt(3) = 4*sqrt(3) + 3*sqrt(3) = 7*sqrt(3)
28/sqrt(8) multiply top and bottom by sqrt(8) = 28*sqrt(8)/[sqrt(8)*sqrt(8)] = 28*sqrt(8)/8 = 7*sqrt(8)/2 But sqrt(8) = sqrt(4*2)= sqrt(4)*sqrt(2) = ±2*sqrt(2) then 7*sqrt(8)/2 = ±7*2*sqrt(2)/2 = ±7*sqrt(2)
1/[5 + 3*sqrt(2)] = [5 - 3*sqrt(2)]/{[5 + 3*sqrt(2)][5 - 3*sqrt(2)]} = [5 + 3*sqrt(2)]/[25 - 18] = [5 - 3*sqrt(2)]/7
y^2 + 4y + 4 = 7 Hence y^2 + 4y -3 = 0 Apply the Quadratic Eq'n y = { - 4 +/- sqrt[(4)^(2) - 4(1)(-3)]} / 2(1) y = { -4 +/- sqrt[ 16 + 12]} / 2 y = { 4 +/- sqrt(28)]}/ 2 y = {4 +/- 5.2915....} /2 y = 9.2915/// / 2 = 4.64575.... & y = -1.2915... / 2 = -0.64575....
No
sqrt(2/49) = sqrt(2)/sqrt(49) = sqrt(2)/7 = 0.20203 (approx).
4
3*sqrt(45) + 7*sqrt(36) = 3*sqrt(9*5) + 7*sqrt(9*4) = 3*sqrt(9)*sqrt(5) + 7*sqrt(9)*sqrt(4) = 3*3*sqrt(5) + 7*3*2 = 9*sqrt(5) + 42 This cannot be simplified further, but it can be evaluated as 62.12461..