Trigonometry Examples

Rationalize the Denominator ( square root of 15xy)/(3 square root of 10xy^3)
Step 1
Combine and into a single radical.
Step 2
Reduce the expression by cancelling the common factors.
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Step 2.1
Cancel the common factor of and .
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Step 2.1.1
Factor out of .
Step 2.1.2
Cancel the common factors.
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Step 2.1.2.1
Factor out of .
Step 2.1.2.2
Cancel the common factor.
Step 2.1.2.3
Rewrite the expression.
Step 2.2
Cancel the common factor of .
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Step 2.2.1
Cancel the common factor.
Step 2.2.2
Rewrite the expression.
Step 2.3
Cancel the common factor of and .
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Step 2.3.1
Factor out of .
Step 2.3.2
Cancel the common factors.
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Step 2.3.2.1
Factor out of .
Step 2.3.2.2
Cancel the common factor.
Step 2.3.2.3
Rewrite the expression.
Step 3
Simplify the numerator.
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Step 3.1
Rewrite as .
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Step 3.1.1
Factor the perfect power out of .
Step 3.1.2
Factor the perfect power out of .
Step 3.1.3
Rearrange the fraction .
Step 3.2
Pull terms out from under the radical.
Step 3.3
Rewrite as .
Step 3.4
Multiply by .
Step 3.5
Combine and simplify the denominator.
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Step 3.5.1
Multiply by .
Step 3.5.2
Raise to the power of .
Step 3.5.3
Raise to the power of .
Step 3.5.4
Use the power rule to combine exponents.
Step 3.5.5
Add and .
Step 3.5.6
Rewrite as .
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Step 3.5.6.1
Use to rewrite as .
Step 3.5.6.2
Apply the power rule and multiply exponents, .
Step 3.5.6.3
Combine and .
Step 3.5.6.4
Cancel the common factor of .
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Step 3.5.6.4.1
Cancel the common factor.
Step 3.5.6.4.2
Rewrite the expression.
Step 3.5.6.5
Evaluate the exponent.
Step 3.6
Simplify the numerator.
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Step 3.6.1
Combine using the product rule for radicals.
Step 3.6.2
Multiply by .
Step 3.7
Multiply by .
Step 3.8
Move to the left of .
Step 4
Multiply the numerator by the reciprocal of the denominator.
Step 5
Multiply .
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Step 5.1
Multiply by .
Step 5.2
Multiply by .