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GED Math : Square Roots and Radicals

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #554 : Ged Math

Solve for $\small y$ $\displaystyle \small y$:

$\small y^2=x-z$ $\displaystyle \small y^2=x-z$

Possible Answers:

$\small y=\sqrt{x-z}$ $\displaystyle \small y=\sqrt{x-z}$

$\small y=x-\sqrt{z}$ $\displaystyle \small y=x-\sqrt{z}$

$\small y=\sqrt{x}-z$ $\displaystyle \small y=\sqrt{x}-z$

$\small y=x^2-z^2$ $\displaystyle \small y=x^2-z^2$

$\small y=\sqrt{x^2-z^2}$ $\displaystyle \small y=\sqrt{x^2-z^2}$

Correct answer:

$\small y=\sqrt{x-z}$ $\displaystyle \small y=\sqrt{x-z}$

Explanation:

In order to solve for $\small y$ $\displaystyle \small y$, we need to move all the variables beside it to the other side of the equation. Luckily for us $\small y$ $\displaystyle \small y$ is all by itself.

Our next step then is to make sure $\small y$ $\displaystyle \small y$ is naked, meaning nothing it attached to it. We can see though that our $\small y$ $\displaystyle \small y$ is being squared, so we need to get rid of that in order to proceed.

In order to get rid of the square, we must square root the whole equation. The square root and square will cancel each other out.

$\small y^2=x-z$ $\displaystyle \small y^2=x-z$

$\small \sqrt{y^2}=\sqrt{x-z}$ $\displaystyle \small \sqrt{y^2}=\sqrt{x-z}$

$\small y=\sqrt{x-z}$ $\displaystyle \small y=\sqrt{x-z}$

Since we don't have any variables that are the same, this is as far as we can go.

Our answer is $\small y=\sqrt{x-z}$ $\displaystyle \small y=\sqrt{x-z}$

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Example Question #221 : Complex Operations

Simplify:

$\sqrt{245}+\sqrt{45}+\sqrt{720}$ $\displaystyle \sqrt{245}+\sqrt{45}+\sqrt{720}$

Possible Answers:

$25\sqrt{3}$ $\displaystyle 25\sqrt{3}$

$29\sqrt{6}$ $\displaystyle 29\sqrt{6}$

$15\sqrt{5}+2\sqrt{3}$ $\displaystyle 15\sqrt{5}+2\sqrt{3}$

$22\sqrt{5}$ $\displaystyle 22\sqrt{5}$

Correct answer:

$22\sqrt{5}$ $\displaystyle 22\sqrt{5}$

Explanation:

Start by simplifying each radical.

$\sqrt{245}=\sqrt{49 \times 5}=7\sqrt{5}$ $\displaystyle \sqrt{245}=\sqrt{49 \times 5}=7\sqrt{5}$

$\sqrt{45}=\sqrt{9 \times 5}=3\sqrt{5}$ $\displaystyle \sqrt{45}=\sqrt{9 \times 5}=3\sqrt{5}$

$\sqrt{720}=\sqrt{144 \times 5}=12\sqrt{5}$ $\displaystyle \sqrt{720}=\sqrt{144 \times 5}=12\sqrt{5}$

The radicals all simplify down into multiples of $\sqrt{5}$ $\displaystyle \sqrt{5}$. You can add them together.

$7\sqrt{5}+3\sqrt{5}+12\sqrt{5}=22\sqrt{5}$ $\displaystyle 7\sqrt{5}+3\sqrt{5}+12\sqrt{5}=22\sqrt{5}$

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GED Math : Square Roots and Radicals

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #554 : Ged Math

Example Question #221 : Complex Operations

All GED Math Resources

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