Trigonometry Examples

Rationalize the Denominator 1/( square root of 1/( square root of x))
Step 1
Simplify the denominator.
Tap for more steps...
Step 1.1
Multiply by .
Step 1.2
Combine and simplify the denominator.
Tap for more steps...
Step 1.2.1
Multiply by .
Step 1.2.2
Raise to the power of .
Step 1.2.3
Raise to the power of .
Step 1.2.4
Use the power rule to combine exponents.
Step 1.2.5
Add and .
Step 1.2.6
Rewrite as .
Tap for more steps...
Step 1.2.6.1
Use to rewrite as .
Step 1.2.6.2
Apply the power rule and multiply exponents, .
Step 1.2.6.3
Combine and .
Step 1.2.6.4
Cancel the common factor of .
Tap for more steps...
Step 1.2.6.4.1
Cancel the common factor.
Step 1.2.6.4.2
Rewrite the expression.
Step 1.2.6.5
Simplify.
Step 1.3
Rewrite as .
Step 1.4
Rewrite as .
Step 1.5
Multiply by .
Step 1.6
Combine and simplify the denominator.
Tap for more steps...
Step 1.6.1
Multiply by .
Step 1.6.2
Raise to the power of .
Step 1.6.3
Raise to the power of .
Step 1.6.4
Use the power rule to combine exponents.
Step 1.6.5
Add and .
Step 1.6.6
Rewrite as .
Tap for more steps...
Step 1.6.6.1
Use to rewrite as .
Step 1.6.6.2
Apply the power rule and multiply exponents, .
Step 1.6.6.3
Combine and .
Step 1.6.6.4
Cancel the common factor of .
Tap for more steps...
Step 1.6.6.4.1
Cancel the common factor.
Step 1.6.6.4.2
Rewrite the expression.
Step 1.6.6.5
Simplify.
Step 1.7
Simplify the numerator.
Tap for more steps...
Step 1.7.1
Rewrite the expression using the least common index of .
Tap for more steps...
Step 1.7.1.1
Use to rewrite as .
Step 1.7.1.2
Rewrite as .
Step 1.7.1.3
Rewrite as .
Step 1.7.2
Combine using the product rule for radicals.
Step 1.7.3
Multiply by by adding the exponents.
Tap for more steps...
Step 1.7.3.1
Multiply by .
Tap for more steps...
Step 1.7.3.1.1
Raise to the power of .
Step 1.7.3.1.2
Use the power rule to combine exponents.
Step 1.7.3.2
Add and .
Step 2
Multiply the numerator by the reciprocal of the denominator.
Step 3
Multiply by .
Step 4
Multiply by .
Step 5
Simplify terms.
Tap for more steps...
Step 5.1
Combine and simplify the denominator.
Tap for more steps...
Step 5.1.1
Multiply by .
Step 5.1.2
Raise to the power of .
Step 5.1.3
Use the power rule to combine exponents.
Step 5.1.4
Add and .
Step 5.1.5
Rewrite as .
Tap for more steps...
Step 5.1.5.1
Use to rewrite as .
Step 5.1.5.2
Apply the power rule and multiply exponents, .
Step 5.1.5.3
Combine and .
Step 5.1.5.4
Multiply by .
Step 5.1.5.5
Cancel the common factor of and .
Tap for more steps...
Step 5.1.5.5.1
Factor out of .
Step 5.1.5.5.2
Cancel the common factors.
Tap for more steps...
Step 5.1.5.5.2.1
Factor out of .
Step 5.1.5.5.2.2
Cancel the common factor.
Step 5.1.5.5.2.3
Rewrite the expression.
Step 5.1.5.5.2.4
Divide by .
Step 5.2
Cancel the common factor of and .
Tap for more steps...
Step 5.2.1
Factor out of .
Step 5.2.2
Cancel the common factors.
Tap for more steps...
Step 5.2.2.1
Factor out of .
Step 5.2.2.2
Cancel the common factor.
Step 5.2.2.3
Rewrite the expression.
Step 6
Simplify the numerator.
Tap for more steps...
Step 6.1
Rewrite as .
Step 6.2
Multiply the exponents in .
Tap for more steps...
Step 6.2.1
Apply the power rule and multiply exponents, .
Step 6.2.2
Multiply by .
Step 6.3
Rewrite as .
Tap for more steps...
Step 6.3.1
Factor out .
Step 6.3.2
Rewrite as .
Step 6.4
Pull terms out from under the radical.
Step 7
Cancel the common factor of .
Tap for more steps...
Step 7.1
Cancel the common factor.
Step 7.2
Divide by .