Pre-Algebra Examples

Graph square root of x^6y^7
Step 1
To remove the radical on the left side of the equation, square both sides of the equation.
Step 2
Simplify each side of the equation.
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Step 2.1
Use to rewrite as .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Multiply the exponents in .
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Step 2.2.1.1.1
Apply the power rule and multiply exponents, .
Step 2.2.1.1.2
Cancel the common factor of .
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Step 2.2.1.1.2.1
Cancel the common factor.
Step 2.2.1.1.2.2
Rewrite the expression.
Step 2.2.1.2
Simplify.
Step 2.3
Simplify the right side.
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Step 2.3.1
Raising to any positive power yields .
Step 3
Solve for .
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Step 3.1
Divide each term in by and simplify.
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Step 3.1.1
Divide each term in by .
Step 3.1.2
Simplify the left side.
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Step 3.1.2.1
Cancel the common factor of .
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Step 3.1.2.1.1
Cancel the common factor.
Step 3.1.2.1.2
Divide by .
Step 3.1.3
Simplify the right side.
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Step 3.1.3.1
Divide by .
Step 3.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.3
Simplify .
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Step 3.3.1
Rewrite as .
Step 3.3.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.3.3
Plus or minus is .
Step 4
To find the end points, substitute the bounds of the values from the domain into .
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Step 4.1
Replace the variable with in the expression.
Step 4.2
The final answer is .
Step 4.3
Replace the variable with in the expression.
Step 4.4
The final answer is .
Step 5
The end points are .
Step 6
The square root can be graphed using the points around the vertex
Step 7