×
  • Disclosure Icon

Simplifying square roots

Enter an equation or problem
Formatting help
Camera input is not recognized!

We think you wrote:

sqrt(275t^8pq^7)

This solution deals with simplifying square roots.

Solution found

5t^4q^3*sqrt(11pq)
5t^4q^3*sqrt(11pq)

Step by Step Solution

More Icon

Simplify :  sqrt(275t8pq7

Step  1  :

Simplify the Integer part of the SQRT

Factor 275 into its prime factors
           275 = 52 • 11 

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 :
           25 = 52 

Factors which will remain inside the root are :
           11 = 11 

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 :
           5 = 5 

At the end of this step the partly simplified SQRT looks like this:
         5 • sqrt (11t8pq7)  

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(t8pq7) = t4q3 • SQRT(pq) 

Combine both simplifications

         sqrt (275t8pq7) =
        5 t4q3 • sqrt(11pq) 


Simplified Root :

      5 t4q3 • sqrt(11pq) 

Why learn this

More Icon