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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

**Exercises on Simplifying Irrational Numbers**

*Simplify the following.*

**1. √322. √7683. √1004. √0.495. √0.00166. √0.257. √368. √19609. √0.003610. -8√0.0411. 4√6412. 7√204813. -9√50714. 12√9915. -6√0.032416. 2√0.016917. -10√0.022518. 5√80**

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**espeon****Real Member**- Registered: 2006-02-05
- Posts: 2,586

do u mean by simplifying them as rounding them?

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,529

Something like this:

1. √32 = √(16 × 2) = √16 × √2 = 4 × √2 = 4√2

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**espeon****Real Member**- Registered: 2006-02-05
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i dont get that.... i thought √ was supposed to find the square root of everythihng

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**justlookingforthemoment****Moderator**- Registered: 2005-05-26
- Posts: 2,161

But it does. √32 is the square root of 32, and 4√64 is the square root of 64 *multiplied* by 7.

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**espeon****Real Member**- Registered: 2006-02-05
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32 being the square root of 32? that doesnt make sense.the square root of 32 is 5.6568542

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

espeon wrote:

32 being the square root of 32? that doesnt make sense.the square root of 32 is 5.6568542

No, no, and no. What √32 is is a surd. √32 = The square root of 32. To simplify a huge surd, we take something like:

√507

√507 = √169 x √3

= 13 x √3

=13√3

Basically, a surd is a square root left in its natural form.

*Last edited by Devanté (2006-09-29 18:50:10)*

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**justlookingforthemoment****Moderator**- Registered: 2005-05-26
- Posts: 2,161

That's right. It's easier to just write √32 instead of 5.6568542...

As this is the Exercises forum, espeon, it's probably better if you post questions about certain topics you don't understand elsewhere, like in 'Help Me' or 'This is Cool'. These exercises are for people who want to practise solving problems which they already know how to do.

It's great that you want to know more, but please post keep this area of the forum tidy - don't let posts stray too far from the actual problems. This message isn't just aimed at you; it's really for everyone. Thanks.

You can find more out about the questions above at these links:

Squares and square roots - http://www.mathsisfun.com/square-root.html

Surds - http://www.mathsisfun.com/surds.html

Irrational numbers - http://www.mathsisfun.com/irrational-numbers.html

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

Hmm...how about either:

a) The topic is split so that my original message is left for people to practise their exercises

b) I delete this topic and post an identical one with just my post

c) All the messages except for mine are deleted for easier use of the exercises

d) Wait, there is no option d.

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**Kurre****Member**- Registered: 2006-07-18
- Posts: 280

am i correct?:/

*Last edited by Kurre (2006-09-29 20:10:08)*

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

I think so. Depends on what you mean by simplifying. √100 = Square root of 100 = 10. I guess it would work.

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**espeon****Real Member**- Registered: 2006-02-05
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o i get it! so ur just using √32 o signify that its the square root of it.i thought u meant that u have to square it.

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

That's exactly right.

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**jimohrazaq****Member**- Registered: 2006-10-02
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pls what is the square root of 0(zero) and how do we explain it if is other than 0(zero)

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**justlookingforthemoment****Moderator**- Registered: 2005-05-26
- Posts: 2,161

jimohrazag, the square root of zero is zero.

0 x 0 = 0

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