Question

√200y^4=
please answer Tomorrow is my exam​

Answer 1

Simplified Root :      10 y2 • sqrt(2) 

Simplify :  sqrt(200y4) 

Step  1  :Simplify the Integer part of the SQRT

Factor 200 into its prime factors

           200 = 23 • 52 

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

           100 = 22 • 52 

Factors which will remain inside the root are :

           2 = 2 

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

           10 = 2 • 5 

At the end of this step the partly simplified SQRT looks like this: 

         10 • sqrt (2y4)  

Step  2  :Simplify the Variable part of the SQRT

Rules for simplifing variables which may be raised to a power:

   (1) variables with no exponent stay inside the radical

   (2) variables raised to power 1 or (-1) stay inside the radical

   (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

      (3.1) sqrt(x8)=x4

     (3.2) sqrt(x-6)=x-3

    (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

      (4.1) sqrt(x5)=x2•sqrt(x)

     (4.2) sqrt(x-7)=x-3•sqrt(x-1)

 Applying these rules to our case we find out that 

      SQRT(y4) = y2

Combine both simplifications

         sqrt (200y4) =

        10 y2 • sqrt(2) 

Simplified Root :      10 y2 • sqrt(2) 

Answer 2

HERE IS YOUR ANSWER ➡

$\sqrt{200 {y}^{4} }$
make factors of 200......
$\sqrt{2 \times 2 \times 5 \times 5 \times 2 {y}^{4} }$
$2 \times5 \sqrt{2 {y}^{4} }$
$10 \sqrt{2 {y}^{4} }$

to simplify more u can write .........

10×y²√2

(as y⁴ has factors y²×y²)

➡10y² √2

HOPE THIS HELPS U.....