Question

find the value of m in 3√1728=3√8 *2*3√3m

Answer 1

Answer:

mark as a brainlist answer

√134(56)

Answer 2

In order to check if a negative number is a perfect cube, first check if the corresponding positive integer is a perfect cube. Also, for any positive integer m, -m3 is the cube of -m.

(i)

On factorising 64 into prime factors, we get:

64=2×2×2×2×2×2

On grouping the factors in triples of equal factors, we get:

64={2×2×2}×{2×2×2}

It is evident that the prime factors of 64 can be grouped into triples of equal factors and no factor is left over. Therefore, 64 is a perfect cube. This implies that -64 is also a perfect cube.

Now, collect one factor from each triplet and multiply, we get:

2×2=4

This implies that 64 is a cube of 4.

Thus, -64 is the cube of -4.

(ii)

On factorising 1056 into prime factors, we get:

1056=2×2×2×2×2×3×11

On grouping the factors in triples of equal factors, we get:

1056={2×2×2}×2×2×3×11

It is evident that the prime factors of 1056 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 1056 is not a perfect cube. This implies that -1056 is not a perfect cube as well.

(iii)

On factorising 2197 into prime factors, we get:

2197=13×13×13

On grouping the factors in triples of equal factors, we get:

2197={13×13×13}

It is evident that the prime factors of 2197 can be grouped into triples of equal factors and no factor is left over. Therefore, 2197 is a perfect cube. This implies that -2197 is also a perfect cube.

Now, collect one factor from each triplet and multiply, we get 13.

This implies that 2197 is a cube of 13.

Thus, -2197 is the cube of -13.

(iv)

On factorising 2744 into prime factors, we get:

2744=2×2×2×7×7×7

On grouping the factors in triples of equal factors, we get:

2744={2×2×2}×{7×7×7}

It is evident that the prime factors of 2744 can be grouped into triples of equal factors and no factor is left over. Therefore, 2744 is a perfect cube. This implies that -2744 is also a perfect cube.

Now, collect one factor from each triplet and multiply, we get:

2×7=14

This implies that 2744 is a cube of 14.

Thus, -2744 is the cube of -14.

(v)

On factorising 42875 into prime factors, we get:

42875=5×5×5×7×7×7

On grouping the factors in triples of equal factors, we get:

42875={5×5×5}×{7×7×7}

It is evident that the prime factors of 42875 can be grouped into triples of equal factors and no factor is left over. Therefore, 42875 is a perfect cube. This implies that -42875 is also a perfect cube.

Now, collect one factor from each triplet and multiply, we get:

5×7=35

This implies that 42875 is a cube of 35.

Thus, -42875 is the cube