Trigonometry Examples

Evaluate square root of ( square root of 41-4)/(( square root of 41)/2)
Step 1
Multiply the numerator by the reciprocal of the denominator.
Step 2
Multiply by .
Step 3
Combine and simplify the denominator.
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Step 3.1
Multiply by .
Step 3.2
Raise to the power of .
Step 3.3
Raise to the power of .
Step 3.4
Use the power rule to combine exponents.
Step 3.5
Add and .
Step 3.6
Rewrite as .
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Step 3.6.1
Use to rewrite as .
Step 3.6.2
Apply the power rule and multiply exponents, .
Step 3.6.3
Combine and .
Step 3.6.4
Cancel the common factor of .
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Step 3.6.4.1
Cancel the common factor.
Step 3.6.4.2
Rewrite the expression.
Step 3.6.5
Evaluate the exponent.
Step 4
Apply the distributive property.
Step 5
Multiply .
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Step 5.1
Combine and .
Step 5.2
Raise to the power of .
Step 5.3
Raise to the power of .
Step 5.4
Use the power rule to combine exponents.
Step 5.5
Add and .
Step 6
Multiply .
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Step 6.1
Combine and .
Step 6.2
Multiply by .
Step 7
Combine the numerators over the common denominator.
Step 8
Simplify the numerator.
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Step 8.1
Rewrite as .
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Step 8.1.1
Use to rewrite as .
Step 8.1.2
Apply the power rule and multiply exponents, .
Step 8.1.3
Combine and .
Step 8.1.4
Cancel the common factor of .
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Step 8.1.4.1
Cancel the common factor.
Step 8.1.4.2
Rewrite the expression.
Step 8.1.5
Evaluate the exponent.
Step 8.2
Multiply by .
Step 9
Rewrite as .
Step 10
Multiply by .
Step 11
Combine and simplify the denominator.
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Step 11.1
Multiply by .
Step 11.2
Raise to the power of .
Step 11.3
Raise to the power of .
Step 11.4
Use the power rule to combine exponents.
Step 11.5
Add and .
Step 11.6
Rewrite as .
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Step 11.6.1
Use to rewrite as .
Step 11.6.2
Apply the power rule and multiply exponents, .
Step 11.6.3
Combine and .
Step 11.6.4
Cancel the common factor of .
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Step 11.6.4.1
Cancel the common factor.
Step 11.6.4.2
Rewrite the expression.
Step 11.6.5
Evaluate the exponent.
Step 12
Combine using the product rule for radicals.
Step 13
The result can be shown in multiple forms.
Exact Form:
Decimal Form: