Multiplying Radicals: Where Is My Mistake?

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In this problem, $a=7$ and $b=\sqrt{3a}$. Thus, the correct answer should be $(7)^2-(\sqrt{3}a)^2=49-(3)a=49+3a$. However, the incorrect answer given by the calculator is $49+3a-14\sqrt{3a}$. This could be due to a mistake in the calculation or a misunderstanding of the formula. To solve this problem correctly, one must remember to multiply the two terms within parentheses and not add them. In summary, when solving problems using the formula $(a-b)(a+b)=a^2-b^2$, make sure to properly multiply the terms within parentheses.
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Cuberoot1
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I did this problem on paper but my calculator doesn't agree with the result. Can somebody tell me where I'm going wrong and how to do it right?

(7-sqrt3a)(7+sqrt3a)
= (7-sqrt3a)7+(7-sqrt3a)sqrt3a
= (7•7-7sqrt3a)+(7sqrt3a-sqrt3asqrt3a)
= 49-7sqrt3a+7sqrt3a-3a
= 49+3a-14sqrt3a

Even before I used the calculator something looked wrong, but I can't figure out how to fix it.
 
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  • #2
Cuberoot said:
I did this problem on paper but my calculator doesn't agree with the result. Can somebody tell me where I'm going wrong and how to do it right?

(7-sqrt3a)(7+sqrt3a)
= (7-sqrt3a)7+(7-sqrt3a)sqrt3a
= (7•7-7sqrt3a)+(7sqrt3a-sqrt3asqrt3a)
= 49-7sqrt3a+7sqrt3a-3a
= 49+3a-14sqrt3a

Even before I used the calculator something looked wrong, but I can't figure out how to fix it.

(Wave)

$$(7-\sqrt{3a})(7+\sqrt{3a})=7 \cdot 7+ 7 \sqrt{3a}-7 \sqrt{3a}-(\sqrt{3a})^2=49-(\sqrt{3}a)^2$$
In general, it is known that $(a-b)(a+b)=a^2-b^2$.
 

FAQ: Multiplying Radicals: Where Is My Mistake?

What is the most common mistake people make when multiplying radicals?

The most common mistake people make when multiplying radicals is forgetting to multiply the numbers outside the radical sign (known as the coefficient) as well as the numbers inside the radical sign.

How do I know if I made a mistake when multiplying radicals?

If you are unsure if you made a mistake when multiplying radicals, you can check your answer by simplifying the radical expression. If the simplified expression is not equivalent to the original expression, then you have made a mistake.

Can I simplify the radical expression before multiplying?

Yes, you can simplify the radical expression before multiplying as long as the simplified expression is equivalent to the original expression. This can make the multiplication process easier and reduce the chances of making a mistake.

What happens to the radicals if I am multiplying more than two expressions?

If you are multiplying more than two expressions, you can first multiply any constants (numbers outside the radical sign) and then multiply the numbers inside the radical sign. After that, you can simplify the resulting radical expression if necessary.

Are there any tips for avoiding mistakes when multiplying radicals?

Some tips for avoiding mistakes when multiplying radicals include simplifying the expression before multiplying, double-checking your work, and practicing with different types of radical expressions to become more familiar with the process.

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