Calculating Square Roots – Part 2

Slideshow 4, Mr Richard Sasaki, Room 307

Objectives• Be able to calculate square roots for

fractions and decimals• Be able to compare square roots

Square Roots - RulesLet us consider that has two roots, .

± 𝑥 ∙ ± 𝑦=¿Here, we used the idea that .

We can use this at any time. It can make finding roots of numbers with fractions and decimals easier.

To keep things simple, when we multiply and divide, we consider only positive roots or negative roots, not one of each.

Square Roots - ReviewLast lesson we calculated as .It is difficult to do this mentally, an easier way may be to convert it to an improper fraction.

= ± 32Here, we used the idea that .

√9√4

=¿

We can use this at any time. It can make finding roots of numbers with fractions and decimals easier.

Square Roots - DecimalExampleCalculate . (You may write your answer as a fraction.)

= ± 45√16√25

=¿ =

Calculate . = = = √324

√25=¿± 185

Answers - Easy

±0 .5 ±0 .6±1 .2 ±0 . 4 ±1 .3

Answers - Hard

±1 .5±2 .2±2 .8±1 .8 ±2 .4±2 .7

± 4 .2±7 .6±9 .8±7 .5± 4 .6±6 .6±9 .5±3 .2±8 .7±8 .3±8 .1±5 .4

Comparing RootsAs we know, . This implies that for positive roots, .In the same way…If , then positive roots for all .

All positive real numbers and zero.

Remember, and must be positive! (Roots of negative numbers produce imaginary ones!)

Comparing RootsExamplesPlace an inequality sign between the following. Consider positive roots only.

√8√15¿ 4√13¿Prove that for positive roots .Let , . As , where .

where .

Answers¿ ¿¿ ¿ ¿

Let , . As , where . where .

¿

¿ ¿¿ ¿ ¿

Let , . As , where . where .