Question
Simplify the expression
n2−811
Evaluate
n2−1−83
Solution
More Steps

Evaluate
−1−83
Reduce fractions to a common denominator
−88−83
Write all numerators above the common denominator
8−8−3
Subtract the numbers
8−11
Use b−a=−ba=−ba to rewrite the fraction
−811
n2−811
Show Solution

Factor the expression
81(8n2−11)
Evaluate
n2−1−83
Subtract the numbers
More Steps

Evaluate
−1−83
Reduce fractions to a common denominator
−88−83
Write all numerators above the common denominator
8−8−3
Subtract the numbers
8−11
Use b−a=−ba=−ba to rewrite the fraction
−811
n2−811
Solution
81(8n2−11)
Show Solution

Find the roots
n1=−422,n2=422
Alternative Form
n1≈−1.172604,n2≈1.172604
Evaluate
n2−1−83
To find the roots of the expression,set the expression equal to 0
n2−1−83=0
Subtract the numbers
More Steps

Simplify
n2−1−83
Subtract the numbers
More Steps

Evaluate
−1−83
Reduce fractions to a common denominator
−88−83
Write all numerators above the common denominator
8−8−3
Subtract the numbers
8−11
Use b−a=−ba=−ba to rewrite the fraction
−811
n2−811
n2−811=0
Move the constant to the right-hand side and change its sign
n2=0+811
Add the terms
n2=811
Take the root of both sides of the equation and remember to use both positive and negative roots
n=±811
Simplify the expression
More Steps

Evaluate
811
To take a root of a fraction,take the root of the numerator and denominator separately
811
Simplify the radical expression
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Evaluate
8
Write the expression as a product where the root of one of the factors can be evaluated
4×2
Write the number in exponential form with the base of 2
22×2
The root of a product is equal to the product of the roots of each factor
22×2
Reduce the index of the radical and exponent with 2
22
2211
Multiply by the Conjugate
22×211×2
Multiply the numbers
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Evaluate
11×2
The product of roots with the same index is equal to the root of the product
11×2
Calculate the product
22
22×222
Multiply the numbers
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Evaluate
22×2
When a square root of an expression is multiplied by itself,the result is that expression
2×2
Multiply the numbers
4
422
n=±422
Separate the equation into 2 possible cases
n=422n=−422
Solution
n1=−422,n2=422
Alternative Form
n1≈−1.172604,n2≈1.172604
Show Solution
