**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)^{2 } = a^{2} + 2ab + b^{2}

a = √5 and b = √3

(√5 + √3)^{2 } = (√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) = a^{2} - b^{2}

(√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) = a^{2} - b^{2}

(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.

- Rationalization of surds
- Comparison of surds
- Operations with radicals
- Ascending and descending order of surds
- Simplifying radical expression
- Exponents and powers

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...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**