SIMPLIFYING RADICALS

Thew following steps will be useful to simplify radicals. 

Step 1 :

Decompose the number inside the radical sign into prime factors.  

Step 2 :

If you have square root (√), you have to take one number out of the square root for every two same numbers multiplied inside the radical.

If you have cube root (3), we have to take one number out of cube root for every three same numbers multiplied inside the radical.

If you have fourth root (4), you have to take one number out of fourth root for every four same numbers multiplied inside the radical.

Step 3 :

Simplify. 

Examples :

Solved Questions

Question 1 : 

Simplify : 

√20

Solution : 

Decompose 20 into prime factors using synthetic division. 

So, we have

√20  =  √(2 ⋅ 2 ⋅ 5)

√20  =  25

Question 2 : 

Simplify : 

√121

Solution : 

Decompose 121 into prime factors.

√121  =  √(11 ⋅ 11)

√121  =  11

Question 3 : 

Simplify : 

√52

Solution : 

Decompose 52 into prime factors using synthetic division.

So, we have

√52  =  √(2 ⋅ 2 ⋅ 13)

√52  =  2√13

Question 4 : 

Simplify : 

√45

Solution : 

Decompose 45 into prime factors using synthetic division.

So, we have

√45  =  √(5 ⋅ 3 ⋅ 3)

√45  =  3√5

Question 5 : 

Simplify : 

3√72

Solution : 

Decompose 72 into prime factors using synthetic division.

So, we have

372  =  3(2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3)

372  =  2 ⋅ 3√(⋅ 3)

372  =  2 ⋅ 3√(⋅ 3)

372  =  23√9

Question 6 : 

Simplify : 

 

3√40

Solution : 

Decompose 40 into prime factors using synthetic division.

So, we have

3√40  =  3(2 ⋅ 2 ⋅ 2 ⋅ 5)

3√40  =  23√5

Question 7 : 

Simplify : 

3√27

Solution : 

Decompose 27 into prime factors using synthetic division.

So, we have

3√27  =  3(3 ⋅ 3 ⋅ 3)

3√27  =  3

Question 8 : 

Simplify : 

 

4√243

Solution : 

Decompose 243 into prime factors using synthetic division.

So, we have

4√243  =  √(3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3)

4√243  =  34√3

Question 9 : 

Simplify : 

5√288

Solution : 

Decompose 288 into prime factors using synthetic division.

So, we have

5288  =  5(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3)

5288  =  2 5√3

Question 10 : 

Simplify : 

6√320

Solution : 

Decompose 320 into prime factors using synthetic division.

So, we have

6320  =  6(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5)

6320  =  26√5

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Dependent System of Linear Equations

    Mar 26, 23 08:27 PM

    dependentsystems
    Dependent System of Linear Equations

    Read More

  2. Dependent Pair of Linear Equations Worksheet

    Mar 26, 23 08:26 PM

    tutoring.png
    Dependent Pair of Linear Equations Worksheet

    Read More

  3. Twin Prime Numbers

    Mar 24, 23 05:25 AM

    Twin Prime Numbers

    Read More