Solving Equations with Surds | Get Help Now

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In summary, to solve an equation with surds, isolate the surd on one side of the equation, square both sides to eliminate the surd, and solve for the remaining equation. A surd is a mathematical expression containing a root that cannot be simplified to a whole number or fraction. An example of solving an equation with surds is given by isolating the surd, squaring both sides, and checking the solution. Special rules for solving equations with surds include including both positive and negative square roots when squaring both sides. If the surd cannot be eliminated, there may not be a real solution, and extraneous solutions can be checked by plugging in and testing for validity.
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dyn
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Hi.
This is not a homework question but I saw this equation on an advert for a website.

(x+15)1/2 + x1/2 = 15

I tried squaring both sides of the equation but that didn't help. Can this equation be solved exactly or can it only be solved by iteration ?
Thanks
 
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Try isolating one square root (##\sqrt {...} = ...##) before squaring, afterwards it should be clear how to solve for x.
 
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Thanks for your help. Got the answer now
 

1. How do I solve equations with surds?

To solve an equation with surds, first isolate the surd on one side of the equation. Then, square both sides of the equation to eliminate the surd. Finally, solve the remaining equation to find the value of the variable.

2. What is a surd?

A surd is a mathematical expression that contains a root, such as a square root or cube root, that cannot be simplified to a whole number or fraction.

3. Can you give an example of solving an equation with surds?

Sure, let's say we have the equation √x + 2 = 6. First, we isolate the surd on one side, so we subtract 2 from both sides to get √x = 4. Then, we square both sides to eliminate the surd, giving us x = 16. Finally, we check our solution by plugging it back into the original equation to make sure it works.

4. Are there any special rules for solving equations with surds?

Yes, when squaring both sides of an equation with a surd, it's important to remember to include both the positive and negative square root. This is because when a number is squared, it can have two possible solutions - one positive and one negative.

5. What if the surd in the equation cannot be eliminated?

If the surd cannot be eliminated, the equation may not have a real solution. In this case, you can check for extraneous solutions by plugging in the proposed solution and seeing if it satisfies the original equation. If it does not, then there is no real solution to the equation.

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