Trigonometry Examples

Evaluate square root of ( square root of 145-7)/( square root of 145/2)
Step 1
Simplify the denominator.
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Step 1.1
Rewrite as .
Step 1.2
Multiply by .
Step 1.3
Combine and simplify the denominator.
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Step 1.3.1
Multiply by .
Step 1.3.2
Raise to the power of .
Step 1.3.3
Raise to the power of .
Step 1.3.4
Use the power rule to combine exponents.
Step 1.3.5
Add and .
Step 1.3.6
Rewrite as .
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Step 1.3.6.1
Use to rewrite as .
Step 1.3.6.2
Apply the power rule and multiply exponents, .
Step 1.3.6.3
Combine and .
Step 1.3.6.4
Cancel the common factor of .
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Step 1.3.6.4.1
Cancel the common factor.
Step 1.3.6.4.2
Rewrite the expression.
Step 1.3.6.5
Evaluate the exponent.
Step 1.4
Simplify the numerator.
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Step 1.4.1
Combine using the product rule for radicals.
Step 1.4.2
Multiply by .
Step 2
Multiply the numerator by the reciprocal of the denominator.
Step 3
Multiply by .
Step 4
Combine and simplify the denominator.
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Step 4.1
Multiply by .
Step 4.2
Raise to the power of .
Step 4.3
Raise to the power of .
Step 4.4
Use the power rule to combine exponents.
Step 4.5
Add and .
Step 4.6
Rewrite as .
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Step 4.6.1
Use to rewrite as .
Step 4.6.2
Apply the power rule and multiply exponents, .
Step 4.6.3
Combine and .
Step 4.6.4
Cancel the common factor of .
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Step 4.6.4.1
Cancel the common factor.
Step 4.6.4.2
Rewrite the expression.
Step 4.6.5
Evaluate the exponent.
Step 5
Cancel the common factor of and .
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Step 5.1
Factor out of .
Step 5.2
Cancel the common factors.
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Step 5.2.1
Factor out of .
Step 5.2.2
Cancel the common factor.
Step 5.2.3
Rewrite the expression.
Step 6
Apply the distributive property.
Step 7
Multiply .
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Step 7.1
Combine and .
Step 7.2
Combine using the product rule for radicals.
Step 7.3
Multiply by .
Step 8
Combine fractions.
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Step 8.1
Combine and .
Step 8.2
Combine the numerators over the common denominator.
Step 9
Simplify each term.
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Step 9.1
Rewrite as .
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Step 9.1.1
Factor out of .
Step 9.1.2
Rewrite as .
Step 9.2
Pull terms out from under the radical.
Step 10
Rewrite as .
Step 11
Multiply by .
Step 12
Combine and simplify the denominator.
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Step 12.1
Multiply by .
Step 12.2
Raise to the power of .
Step 12.3
Raise to the power of .
Step 12.4
Use the power rule to combine exponents.
Step 12.5
Add and .
Step 12.6
Rewrite as .
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Step 12.6.1
Use to rewrite as .
Step 12.6.2
Apply the power rule and multiply exponents, .
Step 12.6.3
Combine and .
Step 12.6.4
Cancel the common factor of .
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Step 12.6.4.1
Cancel the common factor.
Step 12.6.4.2
Rewrite the expression.
Step 12.6.5
Evaluate the exponent.
Step 13
Combine using the product rule for radicals.
Step 14
The result can be shown in multiple forms.
Exact Form:
Decimal Form: