Basic Math Examples

Evaluate square root of -27* square root of 3
-273273
Step 1
Rewrite -27 as -1(27).
-1(27)3
Step 2
Rewrite -1(27) as -127.
-1273
Step 3
Rewrite -1 as i.
i273
Step 4
Rewrite 27 as 323.
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Step 4.1
Factor 9 out of 27.
i9(3)3
Step 4.2
Rewrite 9 as 32.
i3233
i3233
Step 5
Pull terms out from under the radical.
i(33)3
Step 6
Move 3 to the left of i.
3i33
Step 7
Multiply 3i33.
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Step 7.1
Raise 3 to the power of 1.
3i(313)
Step 7.2
Raise 3 to the power of 1.
3i(3131)
Step 7.3
Use the power rule aman=am+n to combine exponents.
3i31+1
Step 7.4
Add 1 and 1.
3i32
3i32
Step 8
Rewrite 32 as 3.
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Step 8.1
Use nax=axn to rewrite 3 as 312.
3i(312)2
Step 8.2
Apply the power rule and multiply exponents, (am)n=amn.
3i3122
Step 8.3
Combine 12 and 2.
3i322
Step 8.4
Cancel the common factor of 2.
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Step 8.4.1
Cancel the common factor.
3i322
Step 8.4.2
Rewrite the expression.
3i31
3i31
Step 8.5
Evaluate the exponent.
3i3
3i3
Step 9
Multiply 3 by 3.
9i
 [x2  12  π  xdx ]