Because the radical cancels out the "x".
"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)
√2 x √25 = 1.4142135623731 x 5 = 7.07106781186548
12 radical 6 x 6 radical 6 = 72 x 6 = 432
The property that is essential to solving radical equations is being able to do the opposite function to the radical and to the other side of the equation. This allows you to solve for the variable. For example, sqrt (x) = 125.11 [sqrt (x)]2 = (125.11)2 x = 15652.5121
7 x 2½
2 radical 11 the square root of 44. 44/2 = 22 radical 2 x 22 radical 2 x 2 x 11 Since 2 is under the radical twice you can take it out 2 radical 11
4 x2
√2 x √2 = (√2)2 = 2
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
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.
2 x 2½ x 3½
"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)
sqrt(1) + 3*sqrt(x) = 1 + 3*x^1/2So the antiderivative is x + [3*x^(3/2)]/(3/2) + c = x + 2*x^(3/2) + c where c is the constant of integration.
To find the inverse you switch the x and the y and then solve for y. x=2 radical( y + 3) radical(y + 3) = x/2 y+3= (x/2)² y = (x/2)² -3 So the answer is y = (x/2)² -3
Radical (3x) = radical(x) * radical(3).
The prime factorization of 52 is 2 x 2 x 132 x 2 x 13 = 522 x 2 x 13 = 52
(x - 3) (x - square root of 2) = 0