Question

1)which is not a perfect square a)4900. b)16×10²⁶. c)16000. d)4×10⁸​

Answer 1

$\textbf{Given:}$

$\textsf{Numbers are}$

$\mathsf{a)4900,\;b)16{\times}10^{26},\;c)16000,\;d)4{\times}10^8}$

$\textbf{To find:}$

$\textsf{Which of the given numbers is not a perfect square}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{4900=7^2{\times}10^2=(7{\times}10)^2\;\;a\;perfect\;square}$

$\mathsf{16{\times}10^{26}=4^2{\times}(10^{13})^2=(4{\times}10^{13})^2\;\;a\;perfect\;square}$

$\mathsf{4{\times}10^8=2^2{\times}(10^4)^2=(2{\times}10^4)^2\;\;a\;perfect\;square}$

$\mathsf{16000=4^2{\times}10^3\;not\;a\;perfect\;square}$

$\textbf{Answer:}$

$\textsf{Option (c) is correct}$

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

which is not a perfect square

a) 4900

b) 16 × 10²⁶

c) 16000

d) 4 × 10⁸

CONCEPT TO BE IMPLEMENTED

A number that ends with odd number of zeros can not be a perfect square

EVALUATION

CHECKING FOR OPTION (a)

Here the given number is 4900

Since the number of zeros is 2 which is even

So 4900 can be a perfect square

More precisely square root of 4900 = 70

CHECKING FOR OPTION (b)

Here the given number is 16 × 10²⁶

Since the number of zeros is 26 which is even

So 16 × 10²⁶ can be a perfect square

More precisely square root of 16 × 10²⁶

$= 4 \times {10}^{13}$

CHECKING FOR OPTION (c)

Here the given number is 16000

Since the number of zeros is 3 which is odd

So 16000 can not be a perfect square

CHECKING FOR OPTION (d)

Here the given number is 4 × 10⁸

Since the number of zeros is 8 which is even

So 4 × 10⁸ can be a perfect square

More precisely square root of 4 × 10⁸

$= 2 \times {10}^{4}$

FINAL ANSWER

Hence the correct option is c) 16000

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