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The expression ( 5 \sqrt{3} ) represents five times the square root of three. The square root of three is an irrational number approximately equal to 1.732, so ( 5 \sqrt{3} ) is approximately ( 5 \times 1.732 ), which equals about 8.66. This value is often used in mathematical contexts where exact values are preferred, particularly in geometry and trigonometry.
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What is 3 square root of 45 minus 3 square root of 5?
3*sqrt(45) - 3*sqrt(5) =3*sqrt(9*5) - 3*sqrt(5) = 3*sqrt(9)*sqrt(5) - 3*sqrt(5)= 3*3*sqrt(5) - 3*sqrt(5) (taking the principal root)= 9*sqrt(5) - 3*sqrt(5) = 6*sqrt(5)
What is 14 radical 20 minus 3 radical 125?
14*sqrt(20) - 3*sqrt(125) = 14*sqrt(4*5) - 3*sqrt(25*5) = 14*sqrt(4)*sqrt(5) - 3*sqrt(25)*sqrt(5) = 14*2*sqrt(5) - 3*5*sqrt(5) = 28*sqrt(5) - 15*sqrt(5) = 13*sqrt(5)
How do you find the value of x if x root 2 divided by 5 minus root 3 equals 5 plus root 3?
x*sqrt(2)/{5 - sqrt(3)} = {5 + sqrt(3)} => x*sqrt(2) = {5 + sqrt(3)} * {5 - sqrt(3)} = 25 - 3 = 22 => x = 22/sqrt(2) = 22*sqrt(2)/{sqrt(2)*sqrt(2)} = 22*sqrt(2)/2 = 11*sqrt(2)
Does irrational closed under all fundamental operations?
No.[5 + sqrt(3)] + [1 - sqrt(3)] = 6 is rational[5 + sqrt(3)] - [1 + sqrt(3)] = 4 is rational[5 + sqrt(3)] * [5 - sqrt(3)] = 22 is rationalsqrt(8)/sqrt(2) = +/- 2 is rational.
What is the tangent of 12 degrees?
=(sqrt(3)*(3-sqrt(5))-sqrt(50-22*sqrt(5)))/2
What is 3 square root of 45 minus 3 square root of 5?
3*sqrt(45) - 3*sqrt(5) =3*sqrt(9*5) - 3*sqrt(5) = 3*sqrt(9)*sqrt(5) - 3*sqrt(5)= 3*3*sqrt(5) - 3*sqrt(5) (taking the principal root)= 9*sqrt(5) - 3*sqrt(5) = 6*sqrt(5)
What is 14 radical 20 minus 3 radical 125?
14*sqrt(20) - 3*sqrt(125) = 14*sqrt(4*5) - 3*sqrt(25*5) = 14*sqrt(4)*sqrt(5) - 3*sqrt(25)*sqrt(5) = 14*2*sqrt(5) - 3*5*sqrt(5) = 28*sqrt(5) - 15*sqrt(5) = 13*sqrt(5)
What is the multiplicative inverse of 5 plus 3 square root of 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
How do you find the value of x if x root 2 divided by 5 minus root 3 equals 5 plus root 3?
x*sqrt(2)/{5 - sqrt(3)} = {5 + sqrt(3)} => x*sqrt(2) = {5 + sqrt(3)} * {5 - sqrt(3)} = 25 - 3 = 22 => x = 22/sqrt(2) = 22*sqrt(2)/{sqrt(2)*sqrt(2)} = 22*sqrt(2)/2 = 11*sqrt(2)
Does irrational closed under all fundamental operations?
No.[5 + sqrt(3)] + [1 - sqrt(3)] = 6 is rational[5 + sqrt(3)] - [1 + sqrt(3)] = 4 is rational[5 + sqrt(3)] * [5 - sqrt(3)] = 22 is rationalsqrt(8)/sqrt(2) = +/- 2 is rational.
What is the tangent of 12 degrees?
=(sqrt(3)*(3-sqrt(5))-sqrt(50-22*sqrt(5)))/2
What is the square root of negative 5 plus the square root of negative 20?
sqrt(-5) + sqrt(-20) = sqrt(-5) + sqrt(4)*sqrt(-5)= sqrt(-5) + 2*sqrt(-5) = 3*sqrt(-5)3*sqrt(5)*i or 6.7082*iwhere i is the imaginary square root of -1.
Square root of 5 plus square root of 45?
sqrt(5) + sqrt(45) = sqrt(5) + sqrt(9*5) = sqrt(5) + sqrt(9)*sqrt(5) = sqrt(5) + 3*sqrt(5) = 4*sqrt(5)
How do you simplify square root of 15 divided by square root of 5?
3
What is 3 square root 45 plus 7square root 36?
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..
What is the simplest square radical form for 50 and 3 square root of 8?
sqrt(50) = sqrt(25*2) = sqrt(25)*sqrt(2) = 5*sqrt(2)3*sqrt(8) = 3*sqrt(4*2) = 3*sqrt(4)*sqrt(2) = 3*2*sqrt(2) = 6*sqrt(2).sqrt(50) = sqrt(25*2) = sqrt(25)*sqrt(2) = 5*sqrt(2)3*sqrt(8) = 3*sqrt(4*2) = 3*sqrt(4)*sqrt(2) = 3*2*sqrt(2) = 6*sqrt(2).sqrt(50) = sqrt(25*2) = sqrt(25)*sqrt(2) = 5*sqrt(2)3*sqrt(8) = 3*sqrt(4*2) = 3*sqrt(4)*sqrt(2) = 3*2*sqrt(2) = 6*sqrt(2).sqrt(50) = sqrt(25*2) = sqrt(25)*sqrt(2) = 5*sqrt(2)3*sqrt(8) = 3*sqrt(4*2) = 3*sqrt(4)*sqrt(2) = 3*2*sqrt(2) = 6*sqrt(2).
What is the simplified expression for radical 3 times radical fifteen?
sqrt(3) x sqrt(15) = sqrt( 3 x 15 ) = sqrt( 45 ) = sqrt( 9 x 5 ) = 3 sqrt(5)
