Algebra Examples

Evaluate (9 square root of 2)/( square root of 10+ square root of 18)
Step 1
Simplify the denominator.
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Step 1.1
Rewrite as .
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Step 1.1.1
Factor out of .
Step 1.1.2
Rewrite as .
Step 1.2
Pull terms out from under the radical.
Step 2
Multiply by .
Step 3
Multiply by .
Step 4
Expand the denominator using the FOIL method.
Step 5
Simplify.
Step 6
Group and together.
Step 7
Apply the distributive property.
Step 8
Combine using the product rule for radicals.
Step 9
Multiply .
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Step 9.1
Raise to the power of .
Step 9.2
Raise to the power of .
Step 9.3
Use the power rule to combine exponents.
Step 9.4
Add and .
Step 10
Simplify each term.
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Step 10.1
Multiply by .
Step 10.2
Rewrite as .
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Step 10.2.1
Factor out of .
Step 10.2.2
Rewrite as .
Step 10.3
Pull terms out from under the radical.
Step 10.4
Rewrite as .
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Step 10.4.1
Use to rewrite as .
Step 10.4.2
Apply the power rule and multiply exponents, .
Step 10.4.3
Combine and .
Step 10.4.4
Cancel the common factor of .
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Step 10.4.4.1
Cancel the common factor.
Step 10.4.4.2
Rewrite the expression.
Step 10.4.5
Evaluate the exponent.
Step 10.5
Multiply by .
Step 11
Reduce the expression by cancelling the common factors.
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Step 11.1
Cancel the common factor of and .
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Step 11.1.1
Factor out of .
Step 11.1.2
Cancel the common factors.
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Step 11.1.2.1
Factor out of .
Step 11.1.2.2
Cancel the common factor.
Step 11.1.2.3
Rewrite the expression.
Step 11.2
Move the negative in front of the fraction.
Step 12
The result can be shown in multiple forms.
Exact Form:
Decimal Form: