Question

If 5n = 200 then √5^ n-2 = ?
(A) 10
(b)10√2
(c)5√2
(D) 2√2​

Answer 1

Answer:

10√2 may be thanks hope it is correct

Answer 2

Solution of the given expression is Option D. 2√2

Step-by-step explanation:

It has been given that  $5^{n}=200$

By taking log on both the sides

$log(5^{n})=log(200)$

nlog5 = log200

n(0.699) = 2.301

n =$\frac{2.301}{0.699}$

n = 3.29

Now we have to evaluate $\sqrt{(5)^{n-2} }$

By placing the value of n = 3.29

$\sqrt{(5)^{n-2} }=\sqrt{(5)^{3.29-2} }$

             = $\sqrt{5^{(1.29)} }$

             = $\sqrt{7.97}$

             ≈ $\sqrt{8}$

             = $2\sqrt{2}$

Therefore, Option D. is the answer.

Learn more how to evaluate the expressions from https://brainly.in/question/12714639