By radical, I am assuming that you mean square root, not cube root, quartic root, or otherwise. If this is the case, then we can use fractional exponents to help. Change sqrt(x) to x^(1/2), or x to the one half power. Then we take a radical of a radical which becomes sqrt(x^(1/2)) = (x^(1/2))^(1/2) = x^(1/4). When we raise a power to a power, we multiply exponents. So the answer to the square root of the square root of x is x to the one fourth power, or the 4th root of x.
You can move it up or down by adding a constant, call it c. Let c>0 Y=radical(x)+c move it up c and y= radical(x)-c moves it down c. You can move it to the right by subtracting c inside the radical sign. Let c>0 y=radical (x-c) moves it to the right c units. y=radical (x+c) moves it to the left c units.
It is a quadratic equation and can be rearranged in the form of:- x2-x-6 = 0 (x+2)(x-3) = 0 Solutions: x = -2 and x = 3
x times x to the first power is x to the second power
x to the 5th power times y to the fourth power
"Radical x times radical x" could be interpreted as the square root of x times the square root of x - in which case the product would be x (the number under the radical sign)
12 radical 6 x 6 radical 6 = 72 x 6 = 432
√3 x √21 = √3 x √(3 x 7) = (√3 x √3) x √7) = 3√7
√2 x √2 = (√2)2 = 2
3 sqrt(6) x sqrt(6) = 18
Radical (3x) = radical(x) * radical(3).
Because the radical cancels out the "x".
sqrt(3) x sqrt(15) = sqrt( 3 x 15 ) = sqrt( 45 ) = sqrt( 9 x 5 ) = 3 sqrt(5)
radical(14)*radical(2) = 2*radical(7) Without further information available we will consider only the square roots. The square roots of 14 are +3.741 and -3.741, similarly the square roots of 2 are+1.414 and -1.414 and so we can have four products 1) (+3.741) X (+1.414) = +5.155 2) (-3.741) x (+1.414) = -5.155 3) (+3.741) x (-1.414) = -5.155 4) (-3.741) x (-1.414) = +5.155 Expressions 1 and 4 are equal, expressions 2 and 3 are equal. Hence the product of radical 14 times radical 2 can be +5.155 or -5.155
The simplest radical form of x is just the square root of x.
radical 30
1 over 2 times radical 6