What is the square root of -10 times the root of -40?

Question

What is the square root of -10 times the root of -40?

2 Answers

Impact of this question

2395 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-20T21:01:38

$sqrt(-10)sqrt(-40) = -20$

Explanation:

$sqrt(-10)sqrt(-40) =$
$(sqrt(-10))(sqrt(-40))=$

You can't simply join the roots together, like $sqrt(x)sqrt(y) = sqrt(xy)$ , because that formula only works if $x$ and $y$ aren't both negative. You have to take the negative out of the root first and then multiply then, using the identity $i^2 = -1$ where $i$ is the imaginary unit, we continue like:

$(sqrt(-1)sqrt(10))(sqrt(-1)sqrt(40))=$
$(isqrt(10))(isqrt(40))=$
$(i^2sqrt(10)sqrt(40))=$
$-sqrt(40*10)=$
$-sqrt(4*100)=$
$-20$

Answer 2 · 2015-09-20T21:08:14

$sqrt(-10)sqrt(-40) = -20$

Explanation:

Use these two complex number definitions/rules to simplify the expression: $sqrt(-1) = i$ , and $i^2 =sqrt(-1)^2= -1$

$sqrt(-10)sqrt(-40) =$
$sqrt(-1*10)sqrt(-1*4*10) =$
$sqrt(-1)sqrt(10)sqrt(-1)sqrt(4)sqrt(10) =$
$sqrt(-1)^2 2 sqrt(10)^2 =$
$-1*2*10 = -20$

Science

Math

Humanities

... and beyond

What is the square root of -10 times the root of -40?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question