Xenice
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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.
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username2207531
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Simplifying surds:

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

2) jjust basic volumes of shapes (4/3 pi r^3 for sphere and length * width * height for cube
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username1732491
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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.
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razzor
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(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!
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Xenice
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(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!
Thanks! This was helpful. )

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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zainyyyyy
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(Original post by Xenice)
Thanks! This was helpful. )

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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razzor
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(Original post by Xenice)
Thanks! This was helpful. )

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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Glad it helped you
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