multiply and simplify if possible.
sq root 6x(sq root x - 2 sq root 6)
simplify the expression
2^3 sq root 2x - 4^3 sq root 2x
simplify the expression
5^1/2 * 5^1/2
rewrite ^3 sq root x^n with a fractional exponent
divide and simplify if possible.
sq root(162x^14)/sq root 2x^2
find the solution
sq root -x - 5 + 3 = x
find the solution
^3 sq root (x + 1)^2 + 5 = 69
1. √6x(√x - 2√6) = √6x√x - 2√6√6 = √6x^2 - 2√36x = √6x^2 - 12√x = √(6x^2 - 12x)
2. 2^3√2x - 4^3√2x = 8√2x - 64√2x = -56√2x
3. 5^1/2 * 5^1/2 = 5^(1/2 + 1/2) = 5^1 = 5
4. (√(162x^14))/(√(2x^2)) = √(162x^12) = √(81 * 2x^12) = 9x^6√2
5. √(-x - 5) + 3 = x
√-x - √5 + 3 = x
Since the square root of a negative number is not a real number, there is no real solution for x.
6. ^3√(x + 1)^2 + 5 = 69
^3√(x + 1)^2 = 64
(x + 1)^2 = 64^3
(x + 1)^2 = 262144
x + 1 = ±√262144
x + 1 = ±512
x = -513 or x = 511