Q: Prove that if a number is tripled then its cube is 27 times the cube of the given number?

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the square root of the given number

9 times bigger

If you are given the area you will have to think what do you times with the number you have to get it.

The volume goes up by 9 times

it becomes three times larger

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The word "tripled" means increased by three times.

You can not triple something by using an exponent, except for the case of 3*3 and 3^2 which are coincidentally the same thing. When something is tripled, it is multiplied by three. When using an exponent, a number is multiplied by itself the specified number of times.

3 times

X 3(times 3)

9 times. The score is TRIPLED (x3) and then re-TRIPLED (x3 again), which is the equivalent of multiplying by 9.

The expression XYZ is not a fraction. If you triple X and triple Y then XYZ becomes 9 times as large. (It is tripled, then tripled again.)

9 times larger

If the radius of a sphere is tripled, the surface area increases by (3)2 = 9 times, and the volume increases by (3)3 = 27 times.

the square root of the given number

9 times bigger

If you are given the area you will have to think what do you times with the number you have to get it.

No. A given number need not even be divisible by a given prime.