Question

1. Which of the following numbers are not perfect squares? Give reasons.
(a) 841
(b) 753, (c) 1,285, (d) 1,296 (e) 325 (1) 5,625 (g) 164

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Answer 1

Answer:

841 is a perfect square because it's the square of 29

753 is not a perfect square

1285 is not a perfect square

1296 is a perfect square as it is the square of 36

325 is not a perfect square

5625 is a perfect square as it is the square of 75

164 is not a perfect square

Step-by-step explanation:

the numbers like 1,4,9,16,25....are called perfect squares because they are the square of natural numbers 1,2,3,4,5,...... .

hope this helps you out

Answer 2

Answer:

The numbers 753, 1285, 325, and 164 are not perfect squares.

Step-by-step explanation:

(a) 841

The prime factorisation of 841 is,

841 = $29\times29$

The square of 29 gives the number 841.

Thus, 841 is a perfect square.

(b) 753

The prime factorisation of 753 is,

753 = $3\times251$

Clearly, 753 is not the perfect square.

(c) 1285

The prime factorisation of 1285 is,

1285 = $5\times257$

Observe that 1285 is not the perfect square.

(d) 1296

The prime factorisation of 1296 is,

1296 = $2\times2\times2\times2\times3\times3\times3\times3$

        = $36\times36$

The square of 36 gives the number 1296.

Thus, 1296 is a perfect square.

(e) 325

The prime factorisation of 325 is,

325 = $5\times5\times13$

Clearly, 325 is not the perfect square.

(f) 5625

The prime factorisation of 5625 is,

5625 = $5\times5\times5\times5\times3\times3$

        = $75\times75$

The square of 75 gives the number 5625.

Thus, 5625 is a perfect square.

(g) 164

The prime factorisation of 164 is,

164 = $2\times2\times41$

Clearly, 164 is not the perfect square.

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