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

2414 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-20T21:01:38

$\sqrt{- 10} \sqrt{- 40} = - 20$ $sqrt(-10)sqrt(-40) = -20$

Explanation:

$\sqrt{- 10} \sqrt{- 40} =$ $sqrt(-10)sqrt(-40) =$
$(\sqrt{- 10}) (\sqrt{- 40}) =$ $(sqrt(-10))(sqrt(-40))=$

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

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

Answer 2 · 2015-09-20T21:08:14

$\sqrt{- 10} \sqrt{- 40} = - 20$ $sqrt(-10)sqrt(-40) = -20$

Explanation:

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

$\sqrt{- 10} \sqrt{- 40} =$ $sqrt(-10)sqrt(-40) =$
$\sqrt{- 1 \cdot 10} \sqrt{- 1 \cdot 4 \cdot 10} =$ $sqrt(-1*10)sqrt(-1*4*10) =$
$\sqrt{- 1} \sqrt{10} \sqrt{- 1} \sqrt{4} \sqrt{10} =$ $sqrt(-1)sqrt(10)sqrt(-1)sqrt(4)sqrt(10) =$
${\sqrt{- 1}}^{2} 2 {\sqrt{10}}^{2} =$ $sqrt(-1)^2 2 sqrt(10)^2 =$
$- 1 \cdot 2 \cdot 10 = - 20$ $-1*2*10 = -20$

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