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

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Explanation:

Simplify the first part of the left side

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

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 turns into

We have the common factor of so we can combine like terms on the left side ending up with

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So,

Yes it is possible to express 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

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺