Trigonometry Examples

Evaluate square root of (50 square root of 2)^2+(400+50 square root of 2)^2
Step 1
Simplify by cancelling exponent with radical.
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Step 1.1
Apply the product rule to .
Step 1.2
Raise to the power of .
Step 1.3
Rewrite as .
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Step 1.3.1
Use to rewrite as .
Step 1.3.2
Apply the power rule and multiply exponents, .
Step 1.3.3
Combine and .
Step 1.3.4
Cancel the common factor of .
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Step 1.3.4.1
Cancel the common factor.
Step 1.3.4.2
Rewrite the expression.
Step 1.3.5
Evaluate the exponent.
Step 1.4
Simplify the expression.
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Step 1.4.1
Multiply by .
Step 1.4.2
Rewrite as .
Step 2
Expand using the FOIL Method.
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Step 2.1
Apply the distributive property.
Step 2.2
Apply the distributive property.
Step 2.3
Apply the distributive property.
Step 3
Simplify and combine like terms.
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Step 3.1
Simplify each term.
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Step 3.1.1
Multiply by .
Step 3.1.2
Multiply by .
Step 3.1.3
Multiply by .
Step 3.1.4
Multiply .
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Step 3.1.4.1
Multiply by .
Step 3.1.4.2
Raise to the power of .
Step 3.1.4.3
Raise to the power of .
Step 3.1.4.4
Use the power rule to combine exponents.
Step 3.1.4.5
Add and .
Step 3.1.5
Rewrite as .
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Step 3.1.5.1
Use to rewrite as .
Step 3.1.5.2
Apply the power rule and multiply exponents, .
Step 3.1.5.3
Combine and .
Step 3.1.5.4
Cancel the common factor of .
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Step 3.1.5.4.1
Cancel the common factor.
Step 3.1.5.4.2
Rewrite the expression.
Step 3.1.5.5
Evaluate the exponent.
Step 3.1.6
Multiply by .
Step 3.2
Add and .
Step 3.3
Add and .
Step 4
Add and .
Step 5
Rewrite as .
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Step 5.1
Factor out of .
Step 5.2
Factor out of .
Step 5.3
Factor out of .
Step 5.4
Rewrite as .
Step 6
Pull terms out from under the radical.
Step 7
The result can be shown in multiple forms.
Exact Form:
Decimal Form: