How do you simplify $(2sqrt10)(4sqrt15)$ ?

Question

1606 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-25T00:57:43

See a solution process below:

First, rewrite the expression as:

$(2 * 4)(sqrt(10) * sqrt(15)) => 8(sqrt(10) * sqrt(15))$

Next, use this rule for exponents to combine the radicals:

$sqrt(a) * sqrt(b) = sqrt(a * b)$

$8(sqrt(10) * sqrt(15)) => 8sqrt(10 * 15) => 8sqrt(150)$

We can rewrite this as:

$8sqrt(25 * 6)$

We can use the above rule for radicals in reverse to simplify the radical term:

$sqrt(a * b) = sqrt(a) * sqrt(b)$

$8(sqrt(25 * 6)) = 8(sqrt(25) * sqrt(6)) => 8(5 * sqrt(6)) =>$

$(8 * 5)sqrt(6) =>$

$40sqrt(6)$

How do you simplify (2sqrt10)(4sqrt15)(2sqrt10)(4sqrt15)?