Algebra Examples

Simplify the Radical Expression ( square root of 2+ square root of 5)/( square root of 2- square root of 5)
Step 1
Multiply by .
Step 2
Multiply by .
Step 3
Expand the denominator using the FOIL method.
Step 4
Simplify.
Step 5
Simplify the numerator.
Tap for more steps...
Step 5.1
Raise to the power of .
Step 5.2
Raise to the power of .
Step 5.3
Use the power rule to combine exponents.
Step 5.4
Add and .
Step 6
Rewrite as .
Step 7
Expand using the FOIL Method.
Tap for more steps...
Step 7.1
Apply the distributive property.
Step 7.2
Apply the distributive property.
Step 7.3
Apply the distributive property.
Step 8
Simplify and combine like terms.
Tap for more steps...
Step 8.1
Simplify each term.
Tap for more steps...
Step 8.1.1
Combine using the product rule for radicals.
Step 8.1.2
Multiply by .
Step 8.1.3
Rewrite as .
Step 8.1.4
Pull terms out from under the radical, assuming positive real numbers.
Step 8.1.5
Combine using the product rule for radicals.
Step 8.1.6
Multiply by .
Step 8.1.7
Combine using the product rule for radicals.
Step 8.1.8
Multiply by .
Step 8.1.9
Combine using the product rule for radicals.
Step 8.1.10
Multiply by .
Step 8.1.11
Rewrite as .
Step 8.1.12
Pull terms out from under the radical, assuming positive real numbers.
Step 8.2
Add and .
Step 8.3
Add and .
Step 9
Move the negative in front of the fraction.
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form: