Question

If 18√8 - 8√18 = √n, what is n? Can you express 18√8 - 8√18 as multiples of the same square root?

Answer 1

Step-by-step explanation:

squaring both side

(18√8-8√18)^2=(√n)^2

(18√8)^2+(8√18)^2-(2)(8√18)(18√8)=n

after solving it we will get

3744-3456=n

n=288

Answer 2

Answers:

n = 288

Yes it is possible to express $18\sqrt{8}-8\sqrt{18}$ as multiples of the same square root (12 multiples of $\sqrt{2}$ )

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Explanation:

Simplify the first part of the left side

$18\sqrt{8} = 18\sqrt{4*2}\\\\18\sqrt{8} = 18\sqrt{4}*\sqrt{2}\\\\18\sqrt{8} = 18*2*\sqrt{2}\\\\18\sqrt{8} = 36\sqrt{2}$

And do the same for the second part of the left side

$8\sqrt{18} = 8\sqrt{9*2}\\\\8\sqrt{18} = 8\sqrt{9}*\sqrt{2}\\\\8\sqrt{18} = 8*3*\sqrt{2}\\\\8\sqrt{18} = 24\sqrt{2}$

For each simplification, you are trying to factor the stuff under the square root so that you pull out the largest perfect square factor possible.

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The original equation $18\sqrt{8}-8\sqrt{18} = \sqrt{n}$ turns into $36\sqrt{2}-24\sqrt{2} = \sqrt{n}$

We have the common factor of $\sqrt{2}$ so we can combine like terms on the left side ending up with $12\sqrt{2}$

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So,

$18\sqrt{8}-8\sqrt{18} = \sqrt{n}\\\\36\sqrt{2}-24\sqrt{2} = \sqrt{n}\\\\12\sqrt{2} = \sqrt{n}\\\\\sqrt{n} = 12\sqrt{2}\\\\\left(\sqrt{n}\right)^2 = \left(12\sqrt{2}\right)^2\\\\n = 288$

Yes it is possible to express $18\sqrt{8}-8\sqrt{18}$ as multiples of the same square root. In this case, we can express the left hand side of the original equation as 12 multiples of $\sqrt{2}$