300*square root of 3 + 300*square root of 6 = 1254.462165
Oh, dude, finding the square root of 6 times the square root of 24 is like finding out what's inside a mystery box. You simply multiply the numbers under the square roots together, so it's the square root of 144. That simplifies to 12, because 12 times 12 is 144. Easy peasy, lemon squeezy!
x2 - 6x + 1 = 0 x = [-(-6) +&- square root of [(-6)2 - 4(1)(1)]]/2(1) x = (6 +&- square root of 32)/2 x = [6 +&- 4(square root of 2)]/2 x = 3 +&- 2(square root of 2) x = 3 + 2(square root of 2) or x = 3 - 2(square root of 2) Check:
You must be careful when multiplying square roots of negative numbers; the same rules that apply for normal square roots do NOT apply. I will use shorthand root(x) for the square root of x. For example, root(2) x root(3) = root(2 x 3) = root(6), but you can't do this with square roots of negative numbers. For example: root(-2) x root(-3) = i root(2) x i root(3) = i2 root(6) = (-1) root(6) = -root(6). "i" is the imaginary unit.
√ 9 x √ 6 = 3 x √ 6 = 3 x 2.45 = 7.35 (2dp)
The idea is to take any perfect square out of the square root sign. root(24) = root(4 x 6) = root(4) x root(6) = 2 x root(6).The idea is to take any perfect square out of the square root sign. root(24) = root(4 x 6) = root(4) x root(6) = 2 x root(6).The idea is to take any perfect square out of the square root sign. root(24) = root(4 x 6) = root(4) x root(6) = 2 x root(6).The idea is to take any perfect square out of the square root sign. root(24) = root(4 x 6) = root(4) x root(6) = 2 x root(6).
300*square root of 3 + 300*square root of 6 = 1254.462165
Oh, dude, finding the square root of 6 times the square root of 24 is like finding out what's inside a mystery box. You simply multiply the numbers under the square roots together, so it's the square root of 144. That simplifies to 12, because 12 times 12 is 144. Easy peasy, lemon squeezy!
x2 - 6x + 1 = 0 x = [-(-6) +&- square root of [(-6)2 - 4(1)(1)]]/2(1) x = (6 +&- square root of 32)/2 x = [6 +&- 4(square root of 2)]/2 x = 3 +&- 2(square root of 2) x = 3 + 2(square root of 2) or x = 3 - 2(square root of 2) Check:
That's the same as the square root of 150 or 5√6 . But the square root is multiplied by x-A2 +Bi4 +5/6 √10√15 = √150 = √(25 x 6) = 5√6
You must be careful when multiplying square roots of negative numbers; the same rules that apply for normal square roots do NOT apply. I will use shorthand root(x) for the square root of x. For example, root(2) x root(3) = root(2 x 3) = root(6), but you can't do this with square roots of negative numbers. For example: root(-2) x root(-3) = i root(2) x i root(3) = i2 root(6) = (-1) root(6) = -root(6). "i" is the imaginary unit.
The square root of 6 is an irrational number, approximately equal to 2.44948974278. When you take the square root of 6 and continue to do so to infinity, the number will not converge to a specific value but will approach the square root of 6. This means that as you take the square root of the result repeatedly, the number will get closer and closer to approximately 2.44948974278 but will never exactly reach it.
To simplify the square root of 5 times the square root of 6, you can multiply the two square roots together. This gives you the square root of (5*6), which simplifies to the square root of 30. Therefore, the simplified answer is the square root of 30.
√ 9 x √ 6 = 3 x √ 6 = 3 x 2.45 = 7.35 (2dp)
Let's x be one of the numbers, and y the other number. So, x + y = -8 xy = 6 y = -x - 8 x(-x -8) = 6 -x^2 - 8x = 6 multiply by -1 both sides x^2 + 8x = -6 solve for x by completing the square; x^2 + 8x + 16 = -6 + 16 (x + 4)^2 = 10 x + 4 = square root of 10 x = -4 + square root of 10 or x = -4 - square root of 10 if we continue to solve the system of the equations, we can find the same value for y. Thus the numbers are -4 + square root of 10 and -4 - square root of 10. Check: (-4 + square root of 10) + (-4 - square root of 10) = -4 + square root of 10 - 4 - square root of 10 = -8 (-4 + square root of 10)(-4 - square root of 10) = (-4)^2 - (square root of 10)^2 = 16 - 10 = 6
6 root(2) = root(36) root(2) = root(36 x 2) = root(72).
square root of (6 x 20) = square root of (120) = 10.95