Algebra 5:03 Simplify Radical Expressions

Some factors are perfect squares, ex:

10 has no perfect factor other than 1 12 has a perfect square factor 4. 18 has a perfect square factor of 9

now try to simplify 3√50.

3√50=3√25*2 (remember, think of the factors of 50, and choose the greatest one,) factors of 50 are 1,2,5,10,25, and 50. the only perfect square of 50, other than 1, is 25. =3* √25* √2 =3*5*√2 =15*√2 simplified to =15*√2,

Radical Expression:

An expression that contains a radical sign.

Radicand

An expression under a radical sign

Index(of a radical)

N in a radical expression (n squared b)

You can use the properties of radicals to simplify expressions.

Product property of radicals for real numbers, a is greater than or equal to 0 and b is greater than or equal to 0. AB squared = A squared*B squared. for example. 16 squared= 4squared* 4squared.

A factor of a number is a number that divides into it without a remainder. ex:

The factors of 10 are 1,2 and 5. The factors of 12 are 1,2,3,4,6 and 12. The factors of 18 are 1,2,3,6,9, and 18.

Simplified radical form( of a square root expression)

There are three conditions to check when determining if a square root expression is considered simplified. radicand is not a fraction no radicals in the denominator no perfect square factors.

Quotient property of radicals

for real numbers, a is greater than or equal to 0, and b is greater than 0. a over b squared = A squared over B squared,(fraction)

√20 --- 49

√20/49= √20/49 Why do you need to use the quotient property of radicals. The radical expression is not simplified because the radical is a fraction. The square root of the quotient equals the quotient of square roots. =√20/7 What is the square root of 49? Take the square root of the perfect square. The square root of 49 is 7. The expression is still not simplified because the radicand of 20 has a perfect square factor. simplify the numerator =√4*5/7 =√4*√5/7 =2√5/7 simplified is = 2√5 ----- 7

Write an expression in simplified radical form. √80

√80= √16*5 What is the largest perfect square factor of 80? Write the radicand as a product with one of the factors being a perfect square. If there is more than one perfect square factor, choose the largest one. The largest perfect square factor is 80 is 16. THINK ABOUT IT, what are the factors pairs of 80-? 1*80 2*40 4*20 5*16 8*10 1,4, and 16 are all perfect square factors, but 16 is the greatest. Also, 1 is a factor of every number, but that does not help hen it comes to simplifying radicals. Use the product property of radicals =√16*√5 simplify =4√5