What is the square root of 96i?
= sqrt(16) sqrt(6) sqrt(i) = 4 sqrt(6) sqrt(i) Now, how do we find the square root of i? It will be a complex number in the form a + bi such that (a + bi)^2 = i <=> a^2 + 2abi - b^2 = i Now, since i has no real component in the sense that a complex number would (that is, it might be written as 0 + 1i), we can equate the real and imaginary components of our solution this way: a^2 - b^2 = 0 2ab = 1 Then, a = b, and ab = a^2 = b^2 = 1/2, so a = b = ± sqrt(2) / 2. Then, sqrt(i) = ± (sqrt(2) / 2 + sqrt(2) i / 2) -- So, the original expression becomes: 4 sqrt(6) (sqrt(2) / 2 + sqrt(2) i / 2) = 4 sqrt(3) + 4i sqrt(3) = (4 sqrt(3))(1 + i)
Is the square root of 96 a rational number?
No. It's irrational. It cannot be expressed as a fraction of two whole numbers. Because of this, it's decimal places go on forever, and never repeat.
What is 7 and then the square root of 96m cubed?
This would = 7 x (square root of (96m) cubed), which could be rephrased as 7 x (square root (16 x 6m)cubed) which could then be written as: 7x (4 cubed) x (square root of (6m cubed)) then: 7x 64x (square root of (6m cubed))= 448x (square root of (6m cubed))= 448 x (square root (216(m cubed ))) 448 √ (216 (mCUBED))= 448 √ (36x 6 (mCUBED))= 448x6√ (6 (mCUBED))= 2688√ (6 (mCUBED)) FINAL ANSWER