# Maths help

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Hello, could somebody please explain how I could go about solving this question (without using a calculator)

Find the smallest number that 1500 needs to be multiplied by in order to make a square number.

I'm given the options

45,

10,

6,

30,

15

Find the smallest number that 1500 needs to be multiplied by in order to make a square number.

I'm given the options

45,

10,

6,

30,

15

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#2

are any of the options very similar to 1500? perhaps start the same? possibly a different number of 0s on the end? (e.g. 500x5 = 50x50)

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#3

(Original post by

Hello, could somebody please explain how I could go about solving this question (without using a calculator)

Find the smallest number that 1500 needs to be multiplied by in order to make a square number.

I'm given the options

45,

10,

6,

30,

15

**Anholm**)Hello, could somebody please explain how I could go about solving this question (without using a calculator)

Find the smallest number that 1500 needs to be multiplied by in order to make a square number.

I'm given the options

45,

10,

6,

30,

15

1

reply

(Original post by

I would start by finding the prime factors of 1,500, which you can do by dividing by 2 as many ties as possible, then by 3, then by 5 etc. Then have a think about what the indices of the prime factors would need to look like if the number is to have an integer square root.

**old_engineer**)I would start by finding the prime factors of 1,500, which you can do by dividing by 2 as many ties as possible, then by 3, then by 5 etc. Then have a think about what the indices of the prime factors would need to look like if the number is to have an integer square root.

That is fine but I've never been taught where to go from there...

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#5

express 1500 as ? x ? x ? x ? x ? x ?

where the question marks are prime numbers.

that will make it easy.

where the question marks are prime numbers.

that will make it easy.

Last edited by the bear; 1 month ago

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#6

(Original post by

Right, so that would make 5^3 × 3 × 2^2

That is fine but I've never been taught where to go from there...

**Anholm**)Right, so that would make 5^3 × 3 × 2^2

That is fine but I've never been taught where to go from there...

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(Original post by

express 1500 as ? x ? x ? x ? x ? x ?

where the question marks are prime numbers.

that will make it easy.

**the bear**)express 1500 as ? x ? x ? x ? x ? x ?

where the question marks are prime numbers.

that will make it easy.

5×5×5×3×2×2

I guess I then single out the pairs leaving 5×3=15

Is that how it's done or have I just made something up?

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#8

(Original post by

Ok,

5×5×5×3×2×2

I guess I then single out the pairs leaving 5×3=15

Is that how it's done or have I just made something up?

**Anholm**)Ok,

5×5×5×3×2×2

I guess I then single out the pairs leaving 5×3=15

Is that how it's done or have I just made something up?

here we have two groups of 5 x 2, but the remaining factors ( 5 x 3 ) are not yet in equal groups, so we must introduce an extra 5 and an extra 3

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#9

**Anholm**)

Hello, could somebody please explain how I could go about solving this question (without using a calculator)

Find the smallest number that 1500 needs to be multiplied by in order to make a square number.

I'm given the options

45,

10,

6,

30,

15

To get a perfect square, you need an even number of each prime factor. Which prime factors do you need to multiply by to get that?

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#10

**Anholm**)

Ok,

5×5×5×3×2×2

I guess I then single out the pairs leaving 5×3=15

Is that how it's done or have I just made something up?

For bonus marks, calculate the square root of the result, without a calculator.

Last edited by RogerOxon; 1 month ago

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