# Evaluate n^(1/2)+6n^(1/4)-16=0

Evaluate n^(1/2)+6n^(1/4)-16=0
Factor the left side of the equation.
Rewrite as .
Let . Substitute for all occurrences of .
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Replace all occurrences of with .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Set equal to .
Solve for .
Add to both sides of the equation.
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Simplify the exponent.
Simplify the left side.
Simplify .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify.
Simplify the right side.
Raise to the power of .
Set equal to and solve for .
Set equal to .
Solve for .
Subtract from both sides of the equation.
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Simplify the exponent.
Simplify the left side.
Simplify .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify.
Simplify the right side.
Raise to the power of .
The final solution is all the values that make true.
Exclude the solutions that do not make true.
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### Name

Name seven hundred fifty-six million seven hundred sixty-eight thousand one hundred seventy-seven

### Interesting facts

• 756768177 has 8 divisors, whose sum is 849348000
• The reverse of 756768177 is 771867657
• Previous prime number is 9

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 54
• Digital Root 9

### Name

Name one billion six hundred twenty-four million three hundred forty-seven thousand thirty

### Interesting facts

• 1624347030 has 16 divisors, whose sum is 3898432944
• The reverse of 1624347030 is 0307434261
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 30
• Digital Root 3

### Name

Name one billion four hundred thirty-four million eight hundred seven thousand six hundred ten

### Interesting facts

• 1434807610 has 32 divisors, whose sum is 2720952000
• The reverse of 1434807610 is 0167084341
• Previous prime number is 1481

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 34
• Digital Root 7