# Equations with Square Roots

## Use squares and square roots to cancel radicals and solve equations.

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Practice Equations with Square Roots

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To Mars and Back

Credit: NASA
Source: http://commons.wikimedia.org/wiki/File:Mars_atmosphere.jpg

What would a group of astronauts need in order to travel to Mars and back? At the very least, they'd need a ship with enough fuel to escape Earth's orbit, travel to Mars, and then escape Mars's orbit so that they could return home. NASA wants to send astronauts to Mars by 2035. Will a manned mission to the Red Planet be possible? It all comes down to the type of fuel that is used.

#### Leaving Orbit

Escape velocity is the speed a spaceship needs to reach to break free from a planet's gravitational attraction. The equation for escape velocity is \begin{align*}v=\sqrt{\frac{2GM}{R}}\end{align*}, where \begin{align*}G\end{align*} is the universal gravitational constant, \begin{align*}M\end{align*} is the mass of the planet, and \begin{align*}R\end{align*} is the radius of the planet. The more massive a planet, the harder it is to break out of its orbit. Escaping orbit requires a lot of power. If a rocket were to carry enough fuel to escape two different orbits, it would have to be very large and very expensive.

Some scientists believe fusion power could provide the answer. Nuclear fusion, a process in which the nuclei of atoms collide, generates a lot of energy from very little fuel. Nuclear-powered spaceships could travel to Mars and back, completing the entire journey in about 6 months. The only problem is that we're not yet sure how to build a ship that can be powered by nuclear fusion.

Credit: Bruce Irving
Source: http://www.flickr.com/photos/flyingsinger/125791010/

British scientists have proposed sending two rockets to Mars. The first rocket would carry a robot capable of mining Mars for fuel, and the second would carry the astronauts. When they arrive at Mars, the fuel for their trip home would be waiting at their destination. Right now, several nations and private companies are all working to send people to Mars. Each group has different ideas for how to make the trip. But perhaps in a just few decades, there will be human beings walking and living on another world.

See for yourself: http://www.bbc.co.uk/news/science-environment-21608742

#### Explore More

Watch the following videos to learn about Mars's environment and one organization's plans to establish a human colony on the Red Planet.

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