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Basic Math Examples
√3+11-√3⋅√3+1√3+1
Step 1
Step 1.1
Cancel the common factor.
√3+11-√3⋅√3+1√3+1
Step 1.2
Rewrite the expression.
√3+11-√3⋅1
√3+11-√3⋅1
Step 2
Multiply √3+11-√3 by 1.
√3+11-√3
Step 3
Multiply √3+11-√3 by 1+√31+√3.
√3+11-√3⋅1+√31+√3
Step 4
Step 4.1
Multiply √3+11-√3 by 1+√31+√3.
(√3+1)(1+√3)(1-√3)(1+√3)
Step 4.2
Expand the denominator using the FOIL method.
(√3+1)(1+√3)1+√3-√3-√32
Step 4.3
Simplify.
(√3+1)(1+√3)-2
(√3+1)(1+√3)-2
Step 5
Step 5.1
Reorder terms.
(1+√3)(1+√3)-2
Step 5.2
Raise 1+√3 to the power of 1.
(1+√3)1(1+√3)-2
Step 5.3
Raise 1+√3 to the power of 1.
(1+√3)1(1+√3)1-2
Step 5.4
Use the power rule aman=am+n to combine exponents.
(1+√3)1+1-2
Step 5.5
Add 1 and 1.
(1+√3)2-2
(1+√3)2-2
Step 6
Rewrite (1+√3)2 as (1+√3)(1+√3).
(1+√3)(1+√3)-2
Step 7
Step 7.1
Apply the distributive property.
1(1+√3)+√3(1+√3)-2
Step 7.2
Apply the distributive property.
1⋅1+1√3+√3(1+√3)-2
Step 7.3
Apply the distributive property.
1⋅1+1√3+√3⋅1+√3√3-2
1⋅1+1√3+√3⋅1+√3√3-2
Step 8
Step 8.1
Simplify each term.
Step 8.1.1
Multiply 1 by 1.
1+1√3+√3⋅1+√3√3-2
Step 8.1.2
Multiply √3 by 1.
1+√3+√3⋅1+√3√3-2
Step 8.1.3
Multiply √3 by 1.
1+√3+√3+√3√3-2
Step 8.1.4
Combine using the product rule for radicals.
1+√3+√3+√3⋅3-2
Step 8.1.5
Multiply 3 by 3.
1+√3+√3+√9-2
Step 8.1.6
Rewrite 9 as 32.
1+√3+√3+√32-2
Step 8.1.7
Pull terms out from under the radical, assuming positive real numbers.
1+√3+√3+3-2
1+√3+√3+3-2
Step 8.2
Add 1 and 3.
4+√3+√3-2
Step 8.3
Add √3 and √3.
4+2√3-2
4+2√3-2
Step 9
Step 9.1
Factor 2 out of 4.
2(2)+2√3-2
Step 9.2
Factor 2 out of 2√3.
2(2)+2(√3)-2
Step 9.3
Factor 2 out of 2(2)+2(√3).
2(2+√3)-2
Step 9.4
Move the negative one from the denominator of 2+√3-1.
-1⋅(2+√3)
-1⋅(2+√3)
Step 10
Rewrite -1⋅(2+√3) as -(2+√3).
-(2+√3)
Step 11
Apply the distributive property.
-1⋅2-√3
Step 12
Multiply -1 by 2.
-2-√3
Step 13
The result can be shown in multiple forms.
Exact Form:
-2-√3
Decimal Form:
-3.73205080…