Question

find the smallest whole numberby which512 must be multiplied in order to give a perfect square​

Answer 1

Answer:

The smallest whole no. will be 2

512×2=1024

√1024=32

Answer 2

Answer:

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).

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