# Rearranging an equation, It includes a square root.

• Georgepowell
In summary, to rearrange an equation with a square root, you can isolate the square root, square both sides, and use inverse operations to solve for the variable. You can also move the square root to the other side of the equation by performing inverse operations. If there is a square root in the denominator, you can multiply both the numerator and denominator by the square root. If there are multiple square roots, repeat the same steps for each one. There is also a shortcut called the "squaring method," but it may introduce extraneous solutions.
Georgepowell
I want to find the value of r such that:

sqrt[(r^2)+(110^2)] + r = 160

Is there a way of doing it?

I have found a solution through trial and error (1dp). But I want a method of finding an exact answer.

Thanks

I just found the solution:

r = (675/16) using an online equation solver.

But how do I get to that? Without trial and error?

Doesn't matter anymore, I figured it out:

sqrt(r²+110²) = 160 -r

r² + 110² = (160 - r)²
r² + 110² = 160² - 2*160*r +r²
320r = 160²-110²
r = 13500/320 = 42.1875

## 1. How do I rearrange an equation with a square root?

To rearrange an equation with a square root, you can follow these steps:

• Isolate the square root on one side of the equation by moving all other terms to the other side.
• Square both sides of the equation to eliminate the square root.
• Solve for the variable by using inverse operations.

## 2. Can I move the square root to the other side of the equation?

Yes, you can move the square root to the other side of the equation by performing the inverse operation. For example, if the square root is being added to one side, you can subtract it from both sides. Just make sure to perform the inverse operation on both sides.

## 3. How do I handle a square root in the denominator?

To handle a square root in the denominator, you can multiply both the numerator and denominator by the square root. This will eliminate the square root in the denominator, but it may create a square root in the numerator. You can then follow the steps in question 1 to further simplify the equation.

## 4. What if there are multiple square roots in the equation?

If there are multiple square roots in the equation, you can follow the same steps as in question 1, but you may need to repeat the process for each square root. Remember to perform the inverse operation on both sides for each square root.

## 5. Is there a shortcut for rearranging an equation with a square root?

Yes, there is a shortcut called the "squaring method." This involves squaring both sides of the equation to eliminate the square root, then solving for the variable using inverse operations. However, this method may introduce extraneous solutions, so it's important to check your answer in the original equation to ensure it is valid.

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