Calculate the square root

Question

square root of 3 over square root of 12

 

square root of 2 time square root of 7 times square root of 14

 

and 

square root of 2 over square root of 7 times square root of 14

Answer 1

Question 1

 

√(3) / √(12)

 

 

We can break up √12 by its factors.

 

√(3) / (√4 √3) =

 

√(3) / (2 √3)

 

 

√3  cancel each other out. We end up with

 

1/2

 

 

Question 2

 

√(2) √(7) √(14)

 

 

√14 can be broken down by its factors.

 

√(2) √(7) √(2) √(7)

 

 

When you multiply a square-rooted number by itself, the square-root gets eliminated.  Here is why.

 

√(2) √(2) √(7) √(7) =

 

    √(4)    √(49) =

 

      2 * 7 =

 

       14

 

Try the last one on your own.

 

Answer 2

Part 1: square root of 3 over square root of 12

this expression is √3 ÷ √12 = 1.732 ÷ 3.464 = 0.5

 

Part 2: square root of 2 time square root of 7 times square root of 14

this expression is √2 x √7 x √14 = 1.414 x 2.646 x 3.742 = 14

 

Part 3:  square root of 2 over square root of 7 times square root of 14

this expression is (√2 x √7) x √14  = (1.414/2.646) x 3.742 = 0.534 x 3.742 = 2

Answer 3

√(3)/√(12)

√(3)/√(3)√(4)

cancel the √(3)'s

1/√(4)

1/2

 

√2√7√14

√14√14

14

 

(√2/√7)(√14)

(√2/√7)(√2√7)

cancel the √7's

√2√2

2

Answer 4

1. 12 = 3*4

 

Therefore, √12 = √(3*4) = √3 * √4

 

Therefore √3 / (√3 * √4) = 1/√4 = 1/2

 

2. 14 = 2*7

Therefore, √14 = √(2*7) = √2 * √7

Therefore √2 * √7 * √14 = √14 * √14 = 14

 

3. √2/√7  *  √14

 

= √2/√7  *  √2 * √7

 

= √2/√2 = 1