Question

Find the smallest whole number by which!
512 must be multiplied in order to give a
perfect​

Answer 1

Answer:

8^3=512

so 8 is the number

Answer 2

Answer:

What is the smallest whole number by which 512 must be multiplied to get the perfect square?

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What is the smallest whole number by which 512 must be multiplied to get the perfect square?

Factorization of 512:

512

2 x 256

2 x 2 x 128

2 x 2 x 2 x 64

2 x 2 x 2 x 2 x 32

2 x 2 x 2 x 2 x 2 x 16

2 x 2 x 2 x 2 x 2 x 2 x 8

2 x 2 x 2 x 2 x 2 x 2 x 2 x 4

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Let’s rewrite the nine factors of 2 in exponential form:

(2 to the 5 ) x (2 to the 4)

In order to obtain a perfect square, let’s change the second number:

(2 to the 5) x (2 to the 5)

Our change involves 2 to the first, or 2.

Multiply 512 by 2 to obtain 1024, which is the square of 32 (2 to the fifth).