# Solve for x square root of x<6

x<6
To remove the radical on the left side of the inequality, square both sides of the inequality.
x2<62
Simplify each side of the inequality.
Multiply the exponents in (x12)2.
Apply the power rule and multiply exponents, (am)n=amn.
x12⋅2<62
Cancel the common factor of 2.
Cancel the common factor.
x12⋅2<62
Rewrite the expression.
x1<62
x1<62
x1<62
Simplify.
x<62
Raise 6 to the power of 2.
x<36
x<36
Find the domain of x-6.
Set the radicand in x greater than or equal to 0 to find where the expression is defined.
x≥0
The domain is all values of x that make the expression defined.
[0,∞)
[0,∞)
Use each root to create test intervals.
0<x<36
x>36
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
Test a value on the interval 0<x<36 to see if it makes the inequality true.
Choose a value on the interval 0<x<36 and see if this value makes the original inequality true.
x=2
Replace x with 2 in the original inequality.
2<6
The left side 1.41421356 is less than the right side 6, which means that the given statement is always true.
True
True
Test a value on the interval x>36 to see if it makes the inequality true.
Choose a value on the interval x>36 and see if this value makes the original inequality true.
x=38
Replace x with 38 in the original inequality.
38<6
The left side 6.164414 is not less than the right side 6, which means that the given statement is false.
False
False
Compare the intervals to determine which ones satisfy the original inequality.
0<x<36 True
x>36 False
0<x<36 True
x>36 False
The solution consists of all of the true intervals.
0<x<36
The result can be shown in multiple forms.
Inequality Form:
0<x<36
Interval Notation:
(0,36)
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Solve for x square root of x<6