Question #f2e51

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Answer 1 · 2017-03-24T22:08:17

$(5sqrt(2))/16$

You are looking for ways to split the numbers into squared values that you can 'take outside' the root

For example $25 ->5^2$ so $sqrt(25)=sqrt(5^2)=5$

You can write $sqrt(25/128)$ as $sqrt(25)/sqrt(128)$

If you are ever not sure about roots build a factor tree diagram (sketch) at the side of your work area. Do not forget to label it as rough work.

Tony B

$sqrt(25/128)" "= "sqrt(5^2)/(sqrt(2^2xx2^2xx2^2xx2))$

$=5/(2xx2xx2xxsqrt(2)) = 5/(8sqrt(2))$

Mathematicians do not like roots in the denominator so lets get rid of it.

Multiply by 1 and you do not change the intrinsic value.

$color(green)(5/(8sqrt(2))color(red)(xx1)" "->" "5/(8sqrt(2))color(red)(xxsqrt(2)/sqrt(2))$

$" "color(green)((5sqrt(2))/(8xx2)" "=" "(5sqrt(2))/16)$