Trigonometry Examples

Evaluate square root of 7/5* square root of 3/14
Step 1
Combine and .
Step 2
Simplify the numerator.
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Step 2.1
Rewrite as .
Step 2.2
Multiply by .
Step 2.3
Combine and simplify the denominator.
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Step 2.3.1
Multiply by .
Step 2.3.2
Raise to the power of .
Step 2.3.3
Raise to the power of .
Step 2.3.4
Use the power rule to combine exponents.
Step 2.3.5
Add and .
Step 2.3.6
Rewrite as .
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Step 2.3.6.1
Use to rewrite as .
Step 2.3.6.2
Apply the power rule and multiply exponents, .
Step 2.3.6.3
Combine and .
Step 2.3.6.4
Cancel the common factor of .
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Step 2.3.6.4.1
Cancel the common factor.
Step 2.3.6.4.2
Rewrite the expression.
Step 2.3.6.5
Evaluate the exponent.
Step 2.4
Simplify the numerator.
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Step 2.4.1
Combine using the product rule for radicals.
Step 2.4.2
Multiply by .
Step 3
Simplify terms.
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Step 3.1
Combine and .
Step 3.2
Reduce the expression by cancelling the common factors.
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Step 3.2.1
Factor out of .
Step 3.2.2
Factor out of .
Step 3.2.3
Cancel the common factor.
Step 3.2.4
Rewrite the expression.
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 .
Step 6
Rewrite as .
Step 7
Rewrite as .
Step 8
Multiply by .
Step 9
Combine and simplify the denominator.
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Step 9.1
Multiply by .
Step 9.2
Raise to the power of .
Step 9.3
Raise to the power of .
Step 9.4
Use the power rule to combine exponents.
Step 9.5
Add and .
Step 9.6
Rewrite as .
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Step 9.6.1
Use to rewrite as .
Step 9.6.2
Apply the power rule and multiply exponents, .
Step 9.6.3
Combine and .
Step 9.6.4
Cancel the common factor of .
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Step 9.6.4.1
Cancel the common factor.
Step 9.6.4.2
Rewrite the expression.
Step 9.6.5
Evaluate the exponent.
Step 10
Simplify the numerator.
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Step 10.1
Rewrite the expression using the least common index of .
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Step 10.1.1
Use to rewrite as .
Step 10.1.2
Rewrite as .
Step 10.1.3
Rewrite as .
Step 10.2
Combine using the product rule for radicals.
Step 11
Simplify the numerator.
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Step 11.1
Rewrite as .
Step 11.2
Rewrite as .
Step 11.3
Evaluate the root.
Step 11.4
Pull terms out from under the radical, assuming positive real numbers.
Step 11.5
Raise to the power of .
Step 11.6
Move the decimal point in to the right by place and decrease the power of by .
Step 11.7
Convert from scientific notation.
Step 12
Divide by .