Which number is not a perfect square a.5,329 b.1,280 c.3,600 d.729?

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Which number is not a perfect square a.5,329 b.1,280 c.3,600 d.729?

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Answer 1 · 2015-07-05T15:45:08

$1280$ $1280$ is not a square.

Explanation:

Of course you could use your calculator to find out, but in this case it can be done faster.

A square can never end in an odd number of zeroes. A zero at the end points to a factor $10 or 2 \cdot 5$ $10or2*5$ . In a square all factors are paired, so there should be an even number of zeroes.

BTW: this does not mean that every number ending in two zeroes is a square!

Answer 2 · 2015-07-05T15:49:33

b. $1280$ $1280$ is not a perfect square.

Explanation:

a. $5329 = 73^{2}$ $5329 = 73^2$
b. $1280 = 2^{8} \cdot 5 = {(2^{4})}^{2} \cdot 5 = 16^{2} \cdot 5$ $1280 = 2^8*5 = (2^4)^2*5 = 16^2*5$
c. $3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} = {(2^{2} \cdot 3 \cdot 5)}^{2} = 60^{2}$ $3600 = 2^4*3^2*5^2 = (2^2*3*5)^2 = 60^2$
d. $729 = 3^{6} = {(3^{3})}^{2} = 27^{2}$ $729 = 3^6 = (3^3)^2 = 27^2$

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Which number is not a perfect square a.5,329 b.1,280 c.3,600 d.729?

2 Answers

Explanation:

Explanation:

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