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Maths help ( a few questions)

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1. Hi everyone. I have a few questions, and I would really appreciate some help. Please include explanations as well as answers so I can learn as well.

1. What's the difference between simplifying a surd and expressing the following expressions as a 'multiple of the smallest possible surd'. What would
√45, be for example.

2.See attached file. What topics would I need to look out for this, and how would I go about solving this? (Sorry for the rotated file)

To some people, it may seem really easy - but maths was not my strongest subject and i'm trying to change things around. Thanks in advance.
Attached Images

2. Simplifying surds:

45 = 9x5
so
√ 45 = √9 x √5 = 3√5
3. 1) sorry have no clue,

2) jjust basic volumes of shapes (4/3 pi r^3 for sphere and length * width * height for cube
4. 1. They are the same thing.

2. Work out the volume of both objects and it should be obvious. You need to memorise how to find the volumes of common solids.
5. (Original post by Xenice)
Hi everyone. I have a few questions, and I would really appreciate some help. Please include explanations as well as answers so I can learn as well.

1. What's the difference between simplifying a surd and expressing the following expressions as a 'multiple of the smallest possible surd'. What would
√45, be for example.

2.See attached file. What topics would I need to look out for this, and how would I go about solving this? (Sorry for the rotated file)

To some people, it may seem really easy - but maths was not my strongest subject and i'm trying to change things around. Thanks in advance.
1) To simplify a surd, or as you put it, "express a surd as a multiple of the smallest possible surd", you need to come up with 2 factors of the number (i.e. 2 numbers that multiply to give that number) such that one of those numbers is square.
So, for √45, notice that we have 9 x 5 = 45 (9 is a square number, so we can use this)
so √45 = √9√5 = 3√5

2) You need to know how to find the volume of 3D shapes.
Volume of a cuboid: length x width x depth
Volume of a sphere: 4/3 x pi x r³
Calculate the volume of both shapes (which should be in terms of x) and then compare the two expressions you have to show that one is greater than the other.

I hope this helps!
6. (Original post by razzor)
1) To simplify a surd, or as you put it, "express a surd as a multiple of the smallest possible surd", you need to come up with 2 factors of the number (i.e. 2 numbers that multiply to give that number) such that one of those numbers is square.
So, for √45, notice that we have 9 x 5 = 45 (9 is a square number, so we can use this)
so √45 = √9√5 = 3√5

2) You need to know how to find the volume of 3D shapes.
Volume of a cuboid: length x width x depth
Volume of a sphere: 4/3 x pi x r³
Calculate the volume of both shapes (which should be in terms of x) and then compare the two expressions you have to show that one is greater than the other.

I hope this helps!

Everyone else helped too, but this was the most detailed. Thanks.

(I'll rep tomorrow - no idea how to +rep on phone)

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7. give him rep
(Original post by Xenice)

Everyone else helped too, but this was the most detailed. Thanks.

(I'll rep tomorrow - no idea how to +rep on phone)

Posted from TSR Mobile
8. (Original post by Xenice)

Everyone else helped too, but this was the most detailed. Thanks.

(I'll rep tomorrow - no idea how to +rep on phone)

Posted from TSR Mobile

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