# 5a^2 -64 = 0

You may also convert the difference of two squares into a product, using the following formula, such that:

`x^2 - y^2 = (x - y)(x + y)`

`{(5a^2 - 64 = (sqrt5*a - sqrt 64)(sqrt5*a + sqrt 64)),(5a^2 - 64 = 0):}=> (sqrt5*a - sqrt 64)(sqrt5*a + sqrt 64) = 0 => {(sqrt5*a - sqrt 64 = 0),(sqrt5*a + sqrt 64 = 0):} => {(sqrt5*a = 8),(sqrt5*a =-8):} => {(a = 8/sqrt5),(a =-8/sqrt5):} `

You need to rationalize the denominators, such that:

`{(a = 8sqrt5/5),(a =-8sqrt5/5):} `

Hence, evaluating the values of a, converting the difference of squares into a product, yields `a = 8sqrt5/5` and `a =-8sqrt5/5` .

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Solve `5a^2-64=0`

`5a^2-64=0`  Add 64 to both sides

`5a^2=64`  Divide both sides by 5

`a^2=64/5`  Take the square root of both sides

`a=+-sqrt(64/5)`

Simplify the root: `sqrt(64/5)=sqrt(64)/sqrt(5)=8/sqrt(5)`

Rationalize: `8/sqrt(5)*sqrt(5)/sqrt(5)=(8sqrt(5))/5`

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The solutions to `5a^2-64=0` are `a=+- (8sqrt(5))/5`

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Approved by eNotes Editorial Team