SIMPLIFYING SQUARE ROOT EXPRESSIONS WITH VARIABLES

About "Simplifying square root expressions with variables" 

Simplifying square root expressions with variables :

Here we are going to see how to simplify square root expressions with variables.

The following examples will illustrate the method of simplifying square root expression with variables.

Example 1 :

Simplify (10 + √3) (2 + √5)

Solution :

(10 + √3) (2 + √5)

To find the product of the given expressions, we have to use the distributive property.

  =  (10 + √3) (2 + √5)

  =  10 (2) + 10 √5 + √3 (2) + 3 (√5)

  =  20 + 10 √5 + 2√3 + √(3 ⋅ 5)

  =  20 + 10 √5 + 2√3 + √15

No two terms are not having same radicand, so we cannot combine the terms.

Hence the answer is 20 + 10 √5 + 2√3 + √15.

Example 2 :

Simplify (√5 + √3)2

Solution :

(√5 + √3)2

The given expression exactly matches with the algebraic identity (a + b)2

(a + b) =  a2 + 2ab + b2

a  =  √5  and b  =  √3

(√5 + √3) =  (√5)2 + 2 (√5)(√3) + (√3)2

  =  5 + 2 √(5 ⋅ 3) + 3

  =  5 + 3  + 2 √15

  =  8 + 2 √15

Hence the answer is 8 + 2 √15.

Example 3 :

Simplify (√13 - √2)(√13 + √2)

Solution :

(√13 - √2)(√13 + √2)

The given expression exactly matches with the algebraic identity (a + b)(a - b)

(a + b)(a - b)  =  a2 - b2

(√13 - √2)(√13 + √2)  =  (√13)2 - (√2)2

  =  13 - 12

  =  1

Example 4 :

Simplify (8 + √3)(8 - √3)

Solution :

(8 + √3)(8 - √3)

The given expression exactly matches with the algebraic identity (a + b)(a - b)

(a + b)(a - b)  =  a2 - b2

(8 + √3)(8 - √3)  =  (8)2 - (√3)2

  =  64 - 3

  =  61

Example 5 :

Simplify (5 √3)(8 - 2√5)

Solution :

(5 √3)(8 - 2√5)

To find the product of the given expressions, we have to use the distributive property.

  =  (5 √3)(8 - 2√5)

  =  5 (8) + 5 (-2√5) + √3 (8) + 3 (-2√5)

  =  40 - 10 √5 + 8√3 - 2√(3 ⋅ 5)

  =  40 - 10 √5 + 8√3 - 2√15

No two terms are not having same radicand, so we cannot combine the terms.

Hence the answer is 40 - 10 √5 + 8√3 - 2√15.

Related topics

We hope that the students would have understood the stuff given on "Simplifying square root expressions with variables"

Apart from the stuff given above, if you want to know more about "Simplifying square root expressions with variables"

If you need any other stuff, please use our google custom search here.

HTML Comment Box is loading comments...