How do you simplify $sqrt(16/27)*sqrt(5/3)$ ?

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Answer 1 · 2018-02-05T02:46:57

$color(purple)((4/9) * sqrt5$

To simplify $sqrt(16/27) * sqrt(5/3)$

According to theory of indices,

$a^m * b^m = (a*b)^m$ . Also, $a^m * a^n = a^(m+n)$

Using the above properties,

$sqrt(16/27) * sqrt5/3) = (16/27)^(1/2) * (5/3)^(1/2)$

$=> ((16/27)(5/3))^2 = ((16 * 5) / (27 * 3))^(1/2)$

$=> ((4 * 4 * 5) / (9 * 9))^(1/2) = color(purple)((4/9) * sqrt5$

Answer 2 · 2018-02-05T02:50:00

The answer is $(4sqrt(5))/9$ , or about $0.994$ .

Radicals that are multiplied together can be condensed together if you multiply their radicands (the stuff under the radical):

$sqrt(16/27)*sqrt(5/3)$

$sqrt((16*5)/(27*3))$

$sqrt(80/81)$

$sqrt(80)/sqrt(81)$

$sqrt(16*5)/9$

$(4sqrt(5))/9~~0.99381...$

How do you simplify sqrt(16/27)*sqrt(5/3)sqrt(16/27)*sqrt(5/3)?