How do you solve #(18-n)^(1/2)=(n/8)^(1/2)#?

Answer 1

#n = 16#

The solution to this is much simpler than it might seem at first. Observe that both powers are the same on both sides of the equality. Since the powers are equal and the bases must also be equal, the solution is as follows:

#(18 - n ) = (n/8)#

So solve for #n#:

#18 - n = n/8 => 144 -8n = n => 144 = 9n => n = 144/9=> n=16#

Check:

#(18-16)^(1/2) = (16/8)^(1/2)#

#2^(1/2)= 2^(1/2)#

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Answer 2

Genesis Allen

To solve the equation (18-n)^(1/2) = (n/8)^(1/2), we can square both sides of the equation to eliminate the square roots. This gives us (18-n) = n/8.

Next, we can multiply both sides of the equation by 8 to get rid of the fraction. This yields 8(18-n) = n.

Expanding the left side of the equation gives us 144 - 8n = n.

To isolate the variable, we can add 8n to both sides of the equation, resulting in 144 = 9n.

Finally, we divide both sides of the equation by 9 to solve for n. This gives us n = 16.

Therefore, the solution to the equation (18-n)^(1/2) = (n/8)^(1/2) is n = 16.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.