A symbol used to indicate square of any number is called radical. The number which is under the root is called radicand.

√3 is called square root of 3.

Example 1:

Simplify 72 to the simplest form

To reduce this number to the simplest form we need to split this number as much as possible.

√72 = √(2 x 2 x 2 x 3 x 3)

If any two numbers which are in the root we can take one of them out of the root.

Here we have 2 and 3 twice. So we can take one from the root.

= 2 x 3 √2

= 6 √2

Now we are going to see practice questions. If you are not able to do any of the problems you can just click the solution. In the solution page you can find solution for each problems with detailed explanation. Once you understand the concept you can try the next question on your own.

 Questions Solution

Question 1

√27 + √75 + √108 - √48

 (A) 2 √3 + √2 (B) 5 √3 + √2 (C) 8 √3 + 2 √2

Question 2

7√30 + 2√75 + 5√50

 (A) √30+5√3+5√2 (B) 5√3+5√2 (C) √30+5√2

Question 3

√27 + √105 + √108 + √45

 (A) 4√3 (B) 4√3+√105 (C) √3-5√2

Question 4

√45 + 3√20 + √80 - 4√40

 (A) 9√5-2√10 (B) 11√15 (C) 9√5

Question 5

3√5 + 2√95 + 3√117 - √78

 (A) 2√95+√78 (B) 2√95+9√13-√78 (C) 3√5+2√95+9√13-√78

Question 6

3 √32 - 2√8 + √50

 (A) 9√2 (B) 13√2 (C) 3√2

Question 7

2 √12 - 3√27 - √243

 (A) 4 √3 (B) 14 √3 (C) -14 √3

Question 8

√54 - √2500 - √24

 (A) -√6 - 50 (B) -5√6 - 50 (C) -2√6 - 5

Question 9

√45 - √25 - √80

 (A) - √5 - 3 (B) - √5 - 5 (C) - 2√5 + 5

Question 10

5√95 - 2√50 - 3√180

 (A) 5√95-10√2-18√5 (B) 5√95-18√5 (C) -10√2-18√5

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: