Question

5.1. Is 176 a perfect cube? if not find the smallest number with which it should be multiplied to get a
perfect cube.​

Answer 1

Answer:

No, 176 is not a perfect cube

Step-by-step explanation:

5×5×5=125

6×6×6=216

So, 176 is not a perfect cube.

This is half solution

I don't know the half solution

Sorry for that

Thank-you

Answer 2

The given question is 176 a perfect cube? if not find the smallest number with which it should be multiplied to get a perfect cube.

The perfect cube numbers below 200 are

cube numbers below 200 are 1,8,37,64,125,216.............

Among them, there is no 176.

Therefore 176 is not a perfect cube.

if it is not a perfect cube we have to find the smallest number with which it should be multiplied to get a

perfect cube.

This is found by the concept of prime factorisation.

The prime factor of 176 is

$2 \times 2 \times 2 \times 2 \times 11$

The above number is the prime factor of 176.

among them

$(2 \times 2)(2 \times 2)(11)$

The first 2 are the perfect squares but 11 is a single factor.

so, we can multiply 11 by 11 to make a perfect square.

hence 176 is multiplied by 11 to make a perfect cube

$176 \times 11 = 1936$

$\sqrt[3]{1936} = 11$

Therefore, the number 176 is multiplied by 11 to make it a perfect cube.

# spj2

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