Multiplication Involving Square Roots w1v5

Question 1

Ex 1: Simplify (method 1)

4sr20 * sr80

Answer 1

Start by finding square root of 20
Extract all perfect squares = sr20 = sr4*5
Then by properties of radicals this = sr4.sr5
Which is = 2.sr5

Next sr80
Extract all perfect squares = sr165
By properties of radicals this = sr16sr5
Which is 4.sr5

= 4(2.sr5) (4.sr5)
Now by commutativity we can regroup this as = (4.2.4)(sr5.sr5)
= 32(5) = 160
(N.B Commutativity is grouping like terms)

Question 2

Ex 1: Simplify (method 2)

4sr20 * sr80

Answer 2

Using srA* srB= sr A*B where A and B is greater than 0

= 4 . sr20*80
= 4 . sr1600
= 160

Question 3

Ex 2: Simplify

5sr3+4sr2)(3sr3-2sr2

Answer 3

Step 1 Foiling

= (5sr3)(3sr3)+(5sr3)(-2sr2)+(4sr2)(3sr3)+(4sr2)(-2sr2)
=multiply like terms…in first instance 53 and sr3sr3 which is

15sr9 - 10sr6 +12sr6 - 8sr4 
= 15(3) - 10sr6 +12sr6 -8(2)
= 45 -10sr6 +12sr6 - 16
= combine like terms to get 
= 45-16 ......-10sr6 + 12sr6
Ans = 29 +2sr6